env stringclasses 1 value | prompt stringlengths 203 478 | extra dict |
|---|---|---|
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ())}}}{}}))
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "(({{{{(())}}}{}}))",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "(({{{{(())}}}{}}))",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(({{{{(",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 22669647,
"suffix_sequence": "())}}}{}}))",
"task_type": "reverse",
"total_length": 18,
"trace_id": "5e6f03a6-59d0-4df1-b0dc-e91ddc4e0b74"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ())}}}{}}))\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 7,
"full_sequence": "(({{{{(())}}}{}}))",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(({{{{(",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 22669647,
"suffix_sequence": "())}}}{}}))",
"task_type": "reverse",
"total_length": 18,
"trace_id": "5e6f03a6-59d0-4df1-b0dc-e91ddc4e0b74"
},
"seed": 22669647,
"task_id": 422669647,
"task_type": "dyck_language2"
} |
logic-v2 | Fill in the blank:
_____ + >⟩]⟧>})>>⦄}⟨⟩⟩ = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨{⦃<<({<⟦[⟨<>⟩]⟧>})>>⦄}⟨⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "⟨{⦃<<({<⟦[⟨<>⟩]⟧>})>>⦄}⟨⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{⦃<<({<⟦[⟨<",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 92713795,
"suffix_sequence": ">⟩]⟧>})>>⦄}⟨⟩⟩",
"task_type": "reverse",
"total_length": 26,
"trace_id": "bc728811-615c-41fa-95f2-8af7070db1f5"
},
"question": "Fill in the blank:\n\n_____ + >⟩]⟧>})>>⦄}⟨⟩⟩ = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 12,
"full_sequence": "⟨{⦃<<({<⟦[⟨<>⟩]⟧>})>>⦄}⟨⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{⦃<<({<⟦[⟨<",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 92713795,
"suffix_sequence": ">⟩]⟧>})>>⦄}⟨⟩⟩",
"task_type": "reverse",
"total_length": 26,
"trace_id": "bc728811-615c-41fa-95f2-8af7070db1f5"
},
"seed": 92713795,
"task_id": 492713795,
"task_type": "dyck_language2"
} |
logic-v2 | Q: What opening brackets should precede "[]⦄⟦⟧⦄})>⟨⟩)⟩⦄>]>>⟧⟩⟩⟩" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟨⟨⟦<<[<⦃⟨(<({⦃⦃[]⦄⟦⟧⦄})>⟨⟩)⟩⦄>]>>⟧⟩⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 16,
"full_sequence": "⟨⟨⟨⟦<<[<⦃⟨(<({⦃⦃[]⦄⟦⟧⦄})>⟨⟩)⟩⦄>]>>⟧⟩⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟨⟨⟦<<[<⦃⟨(<({⦃⦃",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 4373800,
"suffix_sequence": "[]⦄⟦⟧⦄})>⟨⟩)⟩⦄>]>>⟧⟩⟩⟩",
"task_type": "reverse",
"total_length": 38,
"trace_id": "405d9bf2-94e2-4b08-b804-694c4cf4921a"
},
"question": "Q: What opening brackets should precede \"[]⦄⟦⟧⦄})>⟨⟩)⟩⦄>]>>⟧⟩⟩⟩\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 16,
"full_sequence": "⟨⟨⟨⟦<<[<⦃⟨(<({⦃⦃[]⦄⟦⟧⦄})>⟨⟩)⟩⦄>]>>⟧⟩⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟨⟨⟦<<[<⦃⟨(<({⦃⦃",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 4373800,
"suffix_sequence": "[]⦄⟦⟧⦄})>⟨⟩)⟩⦄>]>>⟧⟩⟩⟩",
"task_type": "reverse",
"total_length": 38,
"trace_id": "405d9bf2-94e2-4b08-b804-694c4cf4921a"
},
"seed": 4373800,
"task_id": 404373800,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "()]{}{}" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "[()]{}{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 1,
"full_sequence": "[()]{}{}",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 1441041,
"suffix_sequence": "()]{}{}",
"task_type": "reverse",
"total_length": 8,
"trace_id": "70dc0053-96c0-4f53-b5b0-b3500e07280d"
},
"question": "Let S = \"()]{}{}\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 1,
"full_sequence": "[()]{}{}",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 1441041,
"suffix_sequence": "()]{}{}",
"task_type": "reverse",
"total_length": 8,
"trace_id": "70dc0053-96c0-4f53-b5b0-b3500e07280d"
},
"seed": 1441041,
"task_id": 401441041,
"task_type": "dyck_language2"
} |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ())}]{}()]})))]]])]]}]]}}]}}]))])
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "([(([{{[{{[[{[[([[[((({[[{(())}]{}()]})))]]])]]}]]}}]}}]))])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 27,
"full_sequence": "([(([{{[{{[[{[[([[[((({[[{(())}]{}()]})))]]])]]}]]}}]}}]))])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([(([{{[{{[[{[[([[[((({[[{(",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 46656909,
"suffix_sequence": "())}]{}()]})))]]])]]}]]}}]}}]))])",
"task_type": "reverse",
"total_length": 60,
"trace_id": "bfb53970-24f9-4094-b3e0-24be857b29f8"
},
"question": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: ())}]{}()]})))]]])]]}]]}}]}}]))])\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease provide your final answer (the complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 27,
"full_sequence": "([(([{{[{{[[{[[([[[((({[[{(())}]{}()]})))]]])]]}]]}}]}}]))])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([(([{{[{{[[{[[([[[((({[[{(",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 46656909,
"suffix_sequence": "())}]{}()]})))]]])]]}]]}}]}}]))])",
"task_type": "reverse",
"total_length": 60,
"trace_id": "bfb53970-24f9-4094-b3e0-24be857b29f8"
},
"seed": 46656909,
"task_id": 446656909,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "{}}}]<>{}]" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "[[{{{}}}]<>{}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "[[{{{}}}]<>{}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[[{{",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 58161013,
"suffix_sequence": "{}}}]<>{}]",
"task_type": "reverse",
"total_length": 14,
"trace_id": "ad77ab9e-5503-46ad-8086-506856a106ec"
},
"question": "Let S = \"{}}}]<>{}]\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 4,
"full_sequence": "[[{{{}}}]<>{}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[[{{",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 58161013,
"suffix_sequence": "{}}}]<>{}]",
"task_type": "reverse",
"total_length": 14,
"trace_id": "ad77ab9e-5503-46ad-8086-506856a106ec"
},
"seed": 58161013,
"task_id": 458161013,
"task_type": "dyck_language2"
} |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: <>}()⦄⟧}]}⟦⟧>⦄<>⟨⟩⦃⦄⦃⦄⟩{}⦄⦃⦄})⦄⟩}⦄⟩⦄
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⟨⦃{⟨⦃({⦃⟨⦃<{[{⟦⦃{<>}()⦄⟧}]}⟦⟧>⦄<>⟨⟩⦃⦄⦃⦄⟩{}⦄⦃⦄})⦄⟩}⦄⟩⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"full_sequence": "⦃⟨⦃{⟨⦃({⦃⟨⦃<{[{⟦⦃{<>}()⦄⟧}]}⟦⟧>⦄<>⟨⟩⦃⦄⦃⦄⟩{}⦄⦃⦄})⦄⟩}⦄⟩⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⟨⦃{⟨⦃({⦃⟨⦃<{[{⟦⦃{",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 70004297,
"suffix_sequence": "<>}()⦄⟧}]}⟦⟧>⦄<>⟨⟩⦃⦄⦃⦄⟩{}⦄⦃⦄})⦄⟩}⦄⟩⦄",
"task_type": "reverse",
"total_length": 54,
"trace_id": "510711f2-2911-4c07-852d-ec0a3aa66c22"
},
"question": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: <>}()⦄⟧}]}⟦⟧>⦄<>⟨⟩⦃⦄⦃⦄⟩{}⦄⦃⦄})⦄⟩}⦄⟩⦄\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease provide your final answer (the complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 18,
"full_sequence": "⦃⟨⦃{⟨⦃({⦃⟨⦃<{[{⟦⦃{<>}()⦄⟧}]}⟦⟧>⦄<>⟨⟩⦃⦄⦃⦄⟩{}⦄⦃⦄})⦄⟩}⦄⟩⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⟨⦃{⟨⦃({⦃⟨⦃<{[{⟦⦃{",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 70004297,
"suffix_sequence": "<>}()⦄⟧}]}⟦⟧>⦄<>⟨⟩⦃⦄⦃⦄⟩{}⦄⦃⦄})⦄⟩}⦄⟩⦄",
"task_type": "reverse",
"total_length": 54,
"trace_id": "510711f2-2911-4c07-852d-ec0a3aa66c22"
},
"seed": 70004297,
"task_id": 470004297,
"task_type": "dyck_language2"
} |
logic-v2 | Fill in the blank:
_____ + ]]<>⟩⟦⟧()⟦⟧ = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨[[]]<>⟩⟦⟧()⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "⟨[[]]<>⟩⟦⟧()⟦⟧",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[[",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 80562875,
"suffix_sequence": "]]<>⟩⟦⟧()⟦⟧",
"task_type": "reverse",
"total_length": 14,
"trace_id": "ec5dd221-68d1-4a33-943d-b38fe6c0a1da"
},
"question": "Fill in the blank:\n\n_____ + ]]<>⟩⟦⟧()⟦⟧ = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 3,
"full_sequence": "⟨[[]]<>⟩⟦⟧()⟦⟧",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[[",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 80562875,
"suffix_sequence": "]]<>⟩⟦⟧()⟦⟧",
"task_type": "reverse",
"total_length": 14,
"trace_id": "ec5dd221-68d1-4a33-943d-b38fe6c0a1da"
},
"seed": 80562875,
"task_id": 480562875,
"task_type": "dyck_language2"
} |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: )}⟨⟩⟨⟩[]{}
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{()}⟨⟩⟨⟩[]{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "{()}⟨⟩⟨⟩[]{}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{(",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 79278586,
"suffix_sequence": ")}⟨⟩⟨⟩[]{}",
"task_type": "reverse",
"total_length": 12,
"trace_id": "9f8310c5-e93a-4281-a975-f8725eb3cff9"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: )}⟨⟩⟨⟩[]{}\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 2,
"full_sequence": "{()}⟨⟩⟨⟩[]{}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{(",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 79278586,
"suffix_sequence": ")}⟨⟩⟨⟩[]{}",
"task_type": "reverse",
"total_length": 12,
"trace_id": "9f8310c5-e93a-4281-a975-f8725eb3cff9"
},
"seed": 79278586,
"task_id": 479278586,
"task_type": "dyck_language2"
} |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ⟩{}⟨⟩>⟨⟩>)⟧>)⟨⟩<>>⟧}]])⟧⟩]⟧}⟧>
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "<⟦{⟦[⟨⟦([[{⟦<(<⟦(<<⟨⟩{}⟨⟩>⟨⟩>)⟧>)⟨⟩<>>⟧}]])⟧⟩]⟧}⟧>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 20,
"full_sequence": "<⟦{⟦[⟨⟦([[{⟦<(<⟦(<<⟨⟩{}⟨⟩>⟨⟩>)⟧>)⟨⟩<>>⟧}]])⟧⟩]⟧}⟧>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟦{⟦[⟨⟦([[{⟦<(<⟦(<<⟨",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 17170989,
"suffix_sequence": "⟩{}⟨⟩>⟨⟩>)⟧>)⟨⟩<>>⟧}]])⟧⟩]⟧}⟧>",
"task_type": "reverse",
"total_length": 50,
"trace_id": "4b87d3ec-906b-4b67-b879-cc95d6577fb0"
},
"question": "[DYCK LANGUAGE TASK]\n\nINPUT: ⟩{}⟨⟩>⟨⟩>)⟧>)⟨⟩<>>⟧}]])⟧⟩]⟧}⟧>\nDIRECTION: reverse (prepend opening brackets)\n\nCONSTRAINTS:\n- Minimize added brackets\n- Result must be valid Dyck word\n- Preserve input as suffix\n\nPlease provide your final answer in backticks like `answer`."
},
"metadata": {
"fill_length": 20,
"full_sequence": "<⟦{⟦[⟨⟦([[{⟦<(<⟦(<<⟨⟩{}⟨⟩>⟨⟩>)⟧>)⟨⟩<>>⟧}]])⟧⟩]⟧}⟧>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟦{⟦[⟨⟦([[{⟦<(<⟦(<<⟨",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 17170989,
"suffix_sequence": "⟩{}⟨⟩>⟨⟩>)⟧>)⟨⟩<>>⟧}]])⟧⟩]⟧}⟧>",
"task_type": "reverse",
"total_length": 50,
"trace_id": "4b87d3ec-906b-4b67-b879-cc95d6577fb0"
},
"seed": 17170989,
"task_id": 417170989,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"⟩⟨⟩)⦄⟦⟧⦃⦄}]}⟩⦃⦄"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨{[{⦃(⟨⟩⟨⟩)⦄⟦⟧⦃⦄}]}⟩⦃⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "⟨{[{⦃(⟨⟩⟨⟩)⦄⟦⟧⦃⦄}]}⟩⦃⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{[{⦃(⟨",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 38069211,
"suffix_sequence": "⟩⟨⟩)⦄⟦⟧⦃⦄}]}⟩⦃⦄",
"task_type": "reverse",
"total_length": 22,
"trace_id": "e337c837-3c75-4e17-a4d5-88013b6374e1"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\"⟩⟨⟩)⦄⟦⟧⦃⦄}]}⟩⦃⦄\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 7,
"full_sequence": "⟨{[{⦃(⟨⟩⟨⟩)⦄⟦⟧⦃⦄}]}⟩⦃⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨{[{⦃(⟨",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 38069211,
"suffix_sequence": "⟩⟨⟩)⦄⟦⟧⦃⦄}]}⟩⦃⦄",
"task_type": "reverse",
"total_length": 22,
"trace_id": "e337c837-3c75-4e17-a4d5-88013b6374e1"
},
"seed": 38069211,
"task_id": 438069211,
"task_type": "dyck_language2"
} |
logic-v2 | Q: What opening brackets should precede "()⟨⟩][]][]}]⟧⟧⟩(){}⟦⟧⟩]}}⟩>>⟧>" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<⟦<<⟨{{[⟨⟨⟦⟦[{[[()⟨⟩][]][]}]⟧⟧⟩(){}⟦⟧⟩]}}⟩>>⟧>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 16,
"full_sequence": "<⟦<<⟨{{[⟨⟨⟦⟦[{[[()⟨⟩][]][]}]⟧⟧⟩(){}⟦⟧⟩]}}⟩>>⟧>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟦<<⟨{{[⟨⟨⟦⟦[{[[",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 80341965,
"suffix_sequence": "()⟨⟩][]][]}]⟧⟧⟩(){}⟦⟧⟩]}}⟩>>⟧>",
"task_type": "reverse",
"total_length": 46,
"trace_id": "c7c0d234-5fdc-496f-93ea-1a0a8bf54f58"
},
"question": "Q: What opening brackets should precede \"()⟨⟩][]][]}]⟧⟧⟩(){}⟦⟧⟩]}}⟩>>⟧>\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 16,
"full_sequence": "<⟦<<⟨{{[⟨⟨⟦⟦[{[[()⟨⟩][]][]}]⟧⟧⟩(){}⟦⟧⟩]}}⟩>>⟧>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟦<<⟨{{[⟨⟨⟦⟦[{[[",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 80341965,
"suffix_sequence": "()⟨⟩][]][]}]⟧⟧⟩(){}⟦⟧⟩]}}⟩>>⟧>",
"task_type": "reverse",
"total_length": 46,
"trace_id": "c7c0d234-5fdc-496f-93ea-1a0a8bf54f58"
},
"seed": 80341965,
"task_id": 480341965,
"task_type": "dyck_language2"
} |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: }()()⦆⦆⦆}⦅⦆>⟦⟧[]⟧}⦃⦄⦄>{}}⦄()⦄⦆⟧)}⟩
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨{(⟦⦅⦃⦃{<⦃{⟦<{⦅⦅⦅{}()()⦆⦆⦆}⦅⦆>⟦⟧[]⟧}⦃⦄⦄>{}}⦄()⦄⦆⟧)}⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"full_sequence": "⟨{(⟦⦅⦃⦃{<⦃{⟦<{⦅⦅⦅{}()()⦆⦆⦆}⦅⦆>⟦⟧[]⟧}⦃⦄⦄>{}}⦄()⦄⦆⟧)}⟩",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟨{(⟦⦅⦃⦃{<⦃{⟦<{⦅⦅⦅{",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 11455365,
"suffix_sequence": "}()()⦆⦆⦆}⦅⦆>⟦⟧[]⟧}⦃⦄⦄>{}}⦄()⦄⦆⟧)}⟩",
"task_type": "reverse",
"total_length": 52,
"trace_id": "9b50ad77-bd05-4b6a-97f5-2eb82b7d27ac"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: }()()⦆⦆⦆}⦅⦆>⟦⟧[]⟧}⦃⦄⦄>{}}⦄()⦄⦆⟧)}⟩\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 18,
"full_sequence": "⟨{(⟦⦅⦃⦃{<⦃{⟦<{⦅⦅⦅{}()()⦆⦆⦆}⦅⦆>⟦⟧[]⟧}⦃⦄⦄>{}}⦄()⦄⦆⟧)}⟩",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟨{(⟦⦅⦃⦃{<⦃{⟦<{⦅⦅⦅{",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 11455365,
"suffix_sequence": "}()()⦆⦆⦆}⦅⦆>⟦⟧[]⟧}⦃⦄⦄>{}}⦄()⦄⦆⟧)}⟩",
"task_type": "reverse",
"total_length": 52,
"trace_id": "9b50ad77-bd05-4b6a-97f5-2eb82b7d27ac"
},
"seed": 11455365,
"task_id": 411455365,
"task_type": "dyck_language2"
} |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ⟦⟧<>]>>⦆])⟧⦆⟩⦆⟩⦆⟩}⦆
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⦅{⟨⦅⟨⦅⟨⦅⟦([⦅<<[⟦⟧<>]>>⦆])⟧⦆⟩⦆⟩⦆⟩}⦆",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "⦅{⟨⦅⟨⦅⟨⦅⟦([⦅<<[⟦⟧<>]>>⦆])⟧⦆⟩⦆⟩⦆⟩}⦆",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦅{⟨⦅⟨⦅⟨⦅⟦([⦅<<[",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 42356497,
"suffix_sequence": "⟦⟧<>]>>⦆])⟧⦆⟩⦆⟩⦆⟩}⦆",
"task_type": "reverse",
"total_length": 34,
"trace_id": "5109ac01-4f38-406d-a1d9-18fb7aaa9bef"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ⟦⟧<>]>>⦆])⟧⦆⟩⦆⟩⦆⟩}⦆\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 15,
"full_sequence": "⦅{⟨⦅⟨⦅⟨⦅⟦([⦅<<[⟦⟧<>]>>⦆])⟧⦆⟩⦆⟩⦆⟩}⦆",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦅{⟨⦅⟨⦅⟨⦅⟦([⦅<<[",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 42356497,
"suffix_sequence": "⟦⟧<>]>>⦆])⟧⦆⟩⦆⟩⦆⟩}⦆",
"task_type": "reverse",
"total_length": 34,
"trace_id": "5109ac01-4f38-406d-a1d9-18fb7aaa9bef"
},
"seed": 42356497,
"task_id": 442356497,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"{}}]]()()()}})}){}]{}]()]})"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "({[[[({({{[[{{}}]]()()()}})}){}]{}]()]})",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "({[[[({({{[[{{}}]]()()()}})}){}]{}]()]})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({[[[({({{[[{",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 85386420,
"suffix_sequence": "{}}]]()()()}})}){}]{}]()]})",
"task_type": "reverse",
"total_length": 40,
"trace_id": "7a7bbdf9-dade-4634-a125-107e85961bfe"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\"{}}]]()()()}})}){}]{}]()]})\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 13,
"full_sequence": "({[[[({({{[[{{}}]]()()()}})}){}]{}]()]})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({[[[({({{[[{",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 85386420,
"suffix_sequence": "{}}]]()()()}})}){}]{}]()]})",
"task_type": "reverse",
"total_length": 40,
"trace_id": "7a7bbdf9-dade-4634-a125-107e85961bfe"
},
"seed": 85386420,
"task_id": 485386420,
"task_type": "dyck_language2"
} |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ]()()())))}}))}]}))}]]})]})
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "({[({[[{(({[{(({{((([]()()())))}}))}]}))}]]})]})",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 21,
"full_sequence": "({[({[[{(({[{(({{((([]()()())))}}))}]}))}]]})]})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({[({[[{(({[{(({{((([",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 6549089,
"suffix_sequence": "]()()())))}}))}]}))}]]})]})",
"task_type": "reverse",
"total_length": 48,
"trace_id": "a20cb922-8dac-41fe-90eb-ddad64c1ae23"
},
"question": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: ]()()())))}}))}]}))}]]})]})\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease provide your final answer (the complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 21,
"full_sequence": "({[({[[{(({[{(({{((([]()()())))}}))}]}))}]]})]})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({[({[[{(({[{(({{((([",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 6549089,
"suffix_sequence": "]()()())))}}))}]}))}]]})]})",
"task_type": "reverse",
"total_length": 48,
"trace_id": "a20cb922-8dac-41fe-90eb-ddad64c1ae23"
},
"seed": 6549089,
"task_id": 406549089,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "⦄⦅⦆}⟨⟩⦃⦄⟧⟩>⟩⦄⟦⟧⦄]⦆⦄>⟩}⟧" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⟦{⟨<⦃⦅[⦃⦃⟨<⟨⟦{⦃⦄⦅⦆}⟨⟩⦃⦄⟧⟩>⟩⦄⟦⟧⦄]⦆⦄>⟩}⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "⟦{⟨<⦃⦅[⦃⦃⟨<⟨⟦{⦃⦄⦅⦆}⟨⟩⦃⦄⟧⟩>⟩⦄⟦⟧⦄]⦆⦄>⟩}⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟦{⟨<⦃⦅[⦃⦃⟨<⟨⟦{⦃",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 48364315,
"suffix_sequence": "⦄⦅⦆}⟨⟩⦃⦄⟧⟩>⟩⦄⟦⟧⦄]⦆⦄>⟩}⟧",
"task_type": "reverse",
"total_length": 38,
"trace_id": "26d14420-3047-4d4d-ac80-c493784ac82c"
},
"question": "Let S = \"⦄⦅⦆}⟨⟩⦃⦄⟧⟩>⟩⦄⟦⟧⦄]⦆⦄>⟩}⟧\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 15,
"full_sequence": "⟦{⟨<⦃⦅[⦃⦃⟨<⟨⟦{⦃⦄⦅⦆}⟨⟩⦃⦄⟧⟩>⟩⦄⟦⟧⦄]⦆⦄>⟩}⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟦{⟨<⦃⦅[⦃⦃⟨<⟨⟦{⦃",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 48364315,
"suffix_sequence": "⦄⦅⦆}⟨⟩⦃⦄⟧⟩>⟩⦄⟦⟧⦄]⦆⦄>⟩}⟧",
"task_type": "reverse",
"total_length": 38,
"trace_id": "26d14420-3047-4d4d-ac80-c493784ac82c"
},
"seed": 48364315,
"task_id": 448364315,
"task_type": "dyck_language2"
} |
logic-v2 | Fill in the blank:
_____ + >⟧[]⟧]>()⟧<>]<>>⟨⟩><>[]()() = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<<[⟦<[⟦⟦<>⟧[]⟧]>()⟧<>]<>>⟨⟩><>[]()()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "<<[⟦<[⟦⟦<>⟧[]⟧]>()⟧<>]<>>⟨⟩><>[]()()",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<[⟦<[⟦⟦<",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 30953905,
"suffix_sequence": ">⟧[]⟧]>()⟧<>]<>>⟨⟩><>[]()()",
"task_type": "reverse",
"total_length": 36,
"trace_id": "624bc2d4-8d03-4cc9-bf78-c127ae97e5f1"
},
"question": "Fill in the blank:\n\n_____ + >⟧[]⟧]>()⟧<>]<>>⟨⟩><>[]()() = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 9,
"full_sequence": "<<[⟦<[⟦⟦<>⟧[]⟧]>()⟧<>]<>>⟨⟩><>[]()()",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<[⟦<[⟦⟦<",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 30953905,
"suffix_sequence": ">⟧[]⟧]>()⟧<>]<>>⟨⟩><>[]()()",
"task_type": "reverse",
"total_length": 36,
"trace_id": "624bc2d4-8d03-4cc9-bf78-c127ae97e5f1"
},
"seed": 30953905,
"task_id": 430953905,
"task_type": "dyck_language2"
} |
logic-v2 | Fill in the blank:
_____ + }⦄]>)>⦄]⟩ = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨[⦃<(<[⦃{}⦄]>)>⦄]⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "⟨[⦃<(<[⦃{}⦄]>)>⦄]⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[⦃<(<[⦃{",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 12201544,
"suffix_sequence": "}⦄]>)>⦄]⟩",
"task_type": "reverse",
"total_length": 18,
"trace_id": "4be46445-c4c4-4ddd-bdbb-5ba5f9008f92"
},
"question": "Fill in the blank:\n\n_____ + }⦄]>)>⦄]⟩ = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 9,
"full_sequence": "⟨[⦃<(<[⦃{}⦄]>)>⦄]⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[⦃<(<[⦃{",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 12201544,
"suffix_sequence": "}⦄]>)>⦄]⟩",
"task_type": "reverse",
"total_length": 18,
"trace_id": "4be46445-c4c4-4ddd-bdbb-5ba5f9008f92"
},
"seed": 12201544,
"task_id": 412201544,
"task_type": "dyck_language2"
} |
logic-v2 | Q: What opening brackets should precede ")>]>⟩)))]]⟩)>]>⟩>}>⟩}" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{⟨<{<⟨<[<(⟨[[(((⟨<[<()>]>⟩)))]]⟩)>]>⟩>}>⟩}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 21,
"full_sequence": "{⟨<{<⟨<[<(⟨[[(((⟨<[<()>]>⟩)))]]⟩)>]>⟩>}>⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨<{<⟨<[<(⟨[[(((⟨<[<(",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 57189748,
"suffix_sequence": ")>]>⟩)))]]⟩)>]>⟩>}>⟩}",
"task_type": "reverse",
"total_length": 42,
"trace_id": "a395378e-f6e9-409e-bd5d-7cc10949494f"
},
"question": "Q: What opening brackets should precede \")>]>⟩)))]]⟩)>]>⟩>}>⟩}\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 21,
"full_sequence": "{⟨<{<⟨<[<(⟨[[(((⟨<[<()>]>⟩)))]]⟩)>]>⟩>}>⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨<{<⟨<[<(⟨[[(((⟨<[<(",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 57189748,
"suffix_sequence": ")>]>⟩)))]]⟩)>]>⟩>}>⟩}",
"task_type": "reverse",
"total_length": 42,
"trace_id": "a395378e-f6e9-409e-bd5d-7cc10949494f"
},
"seed": 57189748,
"task_id": 457189748,
"task_type": "dyck_language2"
} |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: {})[])}}}]]}>]]))}}}])]
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[([{{{(([[<{[[{{{(({})[])}}}]]}>]]))}}}])]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "[([{{{(([[<{[[{{{(({})[])}}}]]}>]]))}}}])]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[([{{{(([[<{[[{{{((",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 20543975,
"suffix_sequence": "{})[])}}}]]}>]]))}}}])]",
"task_type": "reverse",
"total_length": 42,
"trace_id": "5744c423-5352-4cc9-ae2b-e4b19b8b5e56"
},
"question": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: {})[])}}}]]}>]]))}}}])]\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease provide your final answer (the complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 19,
"full_sequence": "[([{{{(([[<{[[{{{(({})[])}}}]]}>]]))}}}])]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[([{{{(([[<{[[{{{((",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 20543975,
"suffix_sequence": "{})[])}}}]]}>]]))}}}])]",
"task_type": "reverse",
"total_length": 42,
"trace_id": "5744c423-5352-4cc9-ae2b-e4b19b8b5e56"
},
"seed": 20543975,
"task_id": 420543975,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
">⦄]()()}<>⟨⟩>⦃⦄⦄}]⦄<>⟨⟩[]⟩⟨⟩⟩"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟨⦃[{⦃<{[⦃<>⦄]()()}<>⟨⟩>⦃⦄⦄}]⦄<>⟨⟩[]⟩⟨⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "⟨⟨⦃[{⦃<{[⦃<>⦄]()()}<>⟨⟩>⦃⦄⦄}]⦄<>⟨⟩[]⟩⟨⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟨⦃[{⦃<{[⦃<",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 43818758,
"suffix_sequence": ">⦄]()()}<>⟨⟩>⦃⦄⦄}]⦄<>⟨⟩[]⟩⟨⟩⟩",
"task_type": "reverse",
"total_length": 40,
"trace_id": "2b22b481-4c6c-442b-954e-d899c2f3bd37"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\">⦄]()()}<>⟨⟩>⦃⦄⦄}]⦄<>⟨⟩[]⟩⟨⟩⟩\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 11,
"full_sequence": "⟨⟨⦃[{⦃<{[⦃<>⦄]()()}<>⟨⟩>⦃⦄⦄}]⦄<>⟨⟩[]⟩⟨⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟨⦃[{⦃<{[⦃<",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 43818758,
"suffix_sequence": ">⦄]()()}<>⟨⟩>⦃⦄⦄}]⦄<>⟨⟩[]⟩⟨⟩⟩",
"task_type": "reverse",
"total_length": 40,
"trace_id": "2b22b481-4c6c-442b-954e-d899c2f3bd37"
},
"seed": 43818758,
"task_id": 443818758,
"task_type": "dyck_language2"
} |
logic-v2 | Q: What opening brackets should precede ")⦄⦃⦄)⟩()>⟧⟧{}⟩⦄⦄⟩⟩⟦⟧⟩⟩⦄" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⟨⟨⟨⟨⦃⦃⟨⟦⟦<⟨(⦃()⦄⦃⦄)⟩()>⟧⟧{}⟩⦄⦄⟩⟩⟦⟧⟩⟩⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "⦃⟨⟨⟨⟨⦃⦃⟨⟦⟦<⟨(⦃()⦄⦃⦄)⟩()>⟧⟧{}⟩⦄⦄⟩⟩⟦⟧⟩⟩⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⟨⟨⟨⟨⦃⦃⟨⟦⟦<⟨(⦃(",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 23246708,
"suffix_sequence": ")⦄⦃⦄)⟩()>⟧⟧{}⟩⦄⦄⟩⟩⟦⟧⟩⟩⦄",
"task_type": "reverse",
"total_length": 38,
"trace_id": "495faa1c-126b-4ec7-a669-e6a3ec3e14c9"
},
"question": "Q: What opening brackets should precede \")⦄⦃⦄)⟩()>⟧⟧{}⟩⦄⦄⟩⟩⟦⟧⟩⟩⦄\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 15,
"full_sequence": "⦃⟨⟨⟨⟨⦃⦃⟨⟦⟦<⟨(⦃()⦄⦃⦄)⟩()>⟧⟧{}⟩⦄⦄⟩⟩⟦⟧⟩⟩⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⟨⟨⟨⟨⦃⦃⟨⟦⟦<⟨(⦃(",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 23246708,
"suffix_sequence": ")⦄⦃⦄)⟩()>⟧⟧{}⟩⦄⦄⟩⟩⟦⟧⟩⟩⦄",
"task_type": "reverse",
"total_length": 38,
"trace_id": "495faa1c-126b-4ec7-a669-e6a3ec3e14c9"
},
"seed": 23246708,
"task_id": 423246708,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "⟧}⟧⟩)⟩" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⟨(⟨⟦{⟦⟧}⟧⟩)⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "⟨(⟨⟦{⟦⟧}⟧⟩)⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨(⟨⟦{⟦",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 3034846,
"suffix_sequence": "⟧}⟧⟩)⟩",
"task_type": "reverse",
"total_length": 12,
"trace_id": "354f581a-8842-4e2d-8d6c-9e73dddf5d17"
},
"question": "Let S = \"⟧}⟧⟩)⟩\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 6,
"full_sequence": "⟨(⟨⟦{⟦⟧}⟧⟩)⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨(⟨⟦{⟦",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 3034846,
"suffix_sequence": "⟧}⟧⟩)⟩",
"task_type": "reverse",
"total_length": 12,
"trace_id": "354f581a-8842-4e2d-8d6c-9e73dddf5d17"
},
"seed": 3034846,
"task_id": 403034846,
"task_type": "dyck_language2"
} |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ⟨⟩]}>)>)]}
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pairs beyond what is required
Please provide your final answer (the complete valid sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{[(<(<{[⟨⟩]}>)>)]}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "{[(<(<{[⟨⟩]}>)>)]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[(<(<{[",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 64502413,
"suffix_sequence": "⟨⟩]}>)>)]}",
"task_type": "reverse",
"total_length": 18,
"trace_id": "edd6b6f5-5d5c-4f7f-8d5d-ccd333627ba6"
},
"question": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ⟨⟩]}>)>)]}\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do not add any extra bracket pairs beyond what is required\n\nPlease provide your final answer (the complete valid sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 8,
"full_sequence": "{[(<(<{[⟨⟩]}>)>)]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[(<(<{[",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 64502413,
"suffix_sequence": "⟨⟩]}>)>)]}",
"task_type": "reverse",
"total_length": 18,
"trace_id": "edd6b6f5-5d5c-4f7f-8d5d-ccd333627ba6"
},
"seed": 64502413,
"task_id": 464502413,
"task_type": "dyck_language2"
} |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ⟨⟩{}⟧⟦⟧]]⟧]}⟨⟩>
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<{[⟦[[⟦⟨⟩{}⟧⟦⟧]]⟧]}⟨⟩>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "<{[⟦[[⟦⟨⟩{}⟧⟦⟧]]⟧]}⟨⟩>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{[⟦[[⟦",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 39513634,
"suffix_sequence": "⟨⟩{}⟧⟦⟧]]⟧]}⟨⟩>",
"task_type": "reverse",
"total_length": 22,
"trace_id": "b77d7177-20d8-4b2a-b903-7607084f2773"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ⟨⟩{}⟧⟦⟧]]⟧]}⟨⟩>\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 7,
"full_sequence": "<{[⟦[[⟦⟨⟩{}⟧⟦⟧]]⟧]}⟨⟩>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{[⟦[[⟦",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 39513634,
"suffix_sequence": "⟨⟩{}⟧⟦⟧]]⟧]}⟨⟩>",
"task_type": "reverse",
"total_length": 22,
"trace_id": "b77d7177-20d8-4b2a-b903-7607084f2773"
},
"seed": 39513634,
"task_id": 439513634,
"task_type": "dyck_language2"
} |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ])())<>]]]}}]
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[{{[[[(([])())<>]]]}}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "[{{[[[(([])())<>]]]}}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{{[[[(([",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 94901982,
"suffix_sequence": "])())<>]]]}}]",
"task_type": "reverse",
"total_length": 22,
"trace_id": "f8caaa86-fe74-4eef-b3a7-50704e419bb7"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ])())<>]]]}}]\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 9,
"full_sequence": "[{{[[[(([])())<>]]]}}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{{[[[(([",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 94901982,
"suffix_sequence": "])())<>]]]}}]",
"task_type": "reverse",
"total_length": 22,
"trace_id": "f8caaa86-fe74-4eef-b3a7-50704e419bb7"
},
"seed": 94901982,
"task_id": 494901982,
"task_type": "dyck_language2"
} |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: )]()<>
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[()]()<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "[()]()<>",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[(",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 32657274,
"suffix_sequence": ")]()<>",
"task_type": "reverse",
"total_length": 8,
"trace_id": "7aa8ce9c-79dd-43ee-afb9-ec6926fe9603"
},
"question": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: )]()<>\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease provide your final answer (the complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 2,
"full_sequence": "[()]()<>",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[(",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 32657274,
"suffix_sequence": ")]()<>",
"task_type": "reverse",
"total_length": 8,
"trace_id": "7aa8ce9c-79dd-43ee-afb9-ec6926fe9603"
},
"seed": 32657274,
"task_id": 432657274,
"task_type": "dyck_language2"
} |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ()}⟧>⟩⟧>⟩⟧⟧⟧})>)]]⟧⟩>
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<⟨⟦[[(<({⟦⟦⟦⟨<⟦⟨<⟦{()}⟧>⟩⟧>⟩⟧⟧⟧})>)]]⟧⟩>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 19,
"full_sequence": "<⟨⟦[[(<({⟦⟦⟦⟨<⟦⟨<⟦{()}⟧>⟩⟧>⟩⟧⟧⟧})>)]]⟧⟩>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟨⟦[[(<({⟦⟦⟦⟨<⟦⟨<⟦{",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 35333242,
"suffix_sequence": "()}⟧>⟩⟧>⟩⟧⟧⟧})>)]]⟧⟩>",
"task_type": "reverse",
"total_length": 40,
"trace_id": "6c02bfde-854d-4e83-9508-1fa7cb18f742"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ()}⟧>⟩⟧>⟩⟧⟧⟧})>)]]⟧⟩>\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 19,
"full_sequence": "<⟨⟦[[(<({⟦⟦⟦⟨<⟦⟨<⟦{()}⟧>⟩⟧>⟩⟧⟧⟧})>)]]⟧⟩>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟨⟦[[(<({⟦⟦⟦⟨<⟦⟨<⟦{",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 35333242,
"suffix_sequence": "()}⟧>⟩⟧>⟩⟧⟧⟧})>)]]⟧⟩>",
"task_type": "reverse",
"total_length": 40,
"trace_id": "6c02bfde-854d-4e83-9508-1fa7cb18f742"
},
"seed": 35333242,
"task_id": 435333242,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
")⟧){}}⟧>}>}><>"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<{<{<⟦{(⟦()⟧){}}⟧>}>}><>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "<{<{<⟦{(⟦()⟧){}}⟧>}>}><>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{<{<⟦{(⟦(",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 42780342,
"suffix_sequence": ")⟧){}}⟧>}>}><>",
"task_type": "reverse",
"total_length": 24,
"trace_id": "bc722fc7-47d5-49f2-9c47-ccfc317d2cd4"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\")⟧){}}⟧>}>}><>\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 10,
"full_sequence": "<{<{<⟦{(⟦()⟧){}}⟧>}>}><>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<{<{<⟦{(⟦(",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 42780342,
"suffix_sequence": ")⟧){}}⟧>}>}><>",
"task_type": "reverse",
"total_length": 24,
"trace_id": "bc722fc7-47d5-49f2-9c47-ccfc317d2cd4"
},
"seed": 42780342,
"task_id": 442780342,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "⟨⟩)]>⟩}⟧]⟩" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⟨[⟦{⟨<[(⟨⟩)]>⟩}⟧]⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "⟨[⟦{⟨<[(⟨⟩)]>⟩}⟧]⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[⟦{⟨<[(",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 18687965,
"suffix_sequence": "⟨⟩)]>⟩}⟧]⟩",
"task_type": "reverse",
"total_length": 18,
"trace_id": "980c6e71-342d-4d5f-826d-1e32131d2a0e"
},
"question": "Let S = \"⟨⟩)]>⟩}⟧]⟩\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 8,
"full_sequence": "⟨[⟦{⟨<[(⟨⟩)]>⟩}⟧]⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[⟦{⟨<[(",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 18687965,
"suffix_sequence": "⟨⟩)]>⟩}⟧]⟩",
"task_type": "reverse",
"total_length": 18,
"trace_id": "980c6e71-342d-4d5f-826d-1e32131d2a0e"
},
"seed": 18687965,
"task_id": 418687965,
"task_type": "dyck_language2"
} |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: }<>⟦⟧⦃⦄<>)⦄>⦆⦅⦆]⦆)⟩⦄
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pairs beyond what is required
Please provide your final answer (the complete valid sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⟨(⦅[⦅<⦃({}<>⟦⟧⦃⦄<>)⦄>⦆⦅⦆]⦆)⟩⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "⦃⟨(⦅[⦅<⦃({}<>⟦⟧⦃⦄<>)⦄>⦆⦅⦆]⦆)⟩⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦃⟨(⦅[⦅<⦃({",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 16980286,
"suffix_sequence": "}<>⟦⟧⦃⦄<>)⦄>⦆⦅⦆]⦆)⟩⦄",
"task_type": "reverse",
"total_length": 30,
"trace_id": "f5fba458-d372-4606-9e6b-14a9670f8237"
},
"question": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: }<>⟦⟧⦃⦄<>)⦄>⦆⦅⦆]⦆)⟩⦄\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do not add any extra bracket pairs beyond what is required\n\nPlease provide your final answer (the complete valid sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 10,
"full_sequence": "⦃⟨(⦅[⦅<⦃({}<>⟦⟧⦃⦄<>)⦄>⦆⦅⦆]⦆)⟩⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦃⟨(⦅[⦅<⦃({",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 16980286,
"suffix_sequence": "}<>⟦⟧⦃⦄<>)⦄>⦆⦅⦆]⦆)⟩⦄",
"task_type": "reverse",
"total_length": 30,
"trace_id": "f5fba458-d372-4606-9e6b-14a9670f8237"
},
"seed": 16980286,
"task_id": 416980286,
"task_type": "dyck_language2"
} |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ⟩{}⦃⦄⟩()⟦⟧])[]⟧⦃⦄⟨⟩>⦆⟩>)}⟧⦅⦆}⦄<>]>>
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "<<[⦃{⟦{(<⟨⦅<⟦([⟨⟨⟩{}⦃⦄⟩()⟦⟧])[]⟧⦃⦄⟨⟩>⦆⟩>)}⟧⦅⦆}⦄<>]>>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "<<[⦃{⟦{(<⟨⦅<⟦([⟨⟨⟩{}⦃⦄⟩()⟦⟧])[]⟧⦃⦄⟨⟩>⦆⟩>)}⟧⦅⦆}⦄<>]>>",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "<<[⦃{⟦{(<⟨⦅<⟦([⟨⟨",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 65948859,
"suffix_sequence": "⟩{}⦃⦄⟩()⟦⟧])[]⟧⦃⦄⟨⟩>⦆⟩>)}⟧⦅⦆}⦄<>]>>",
"task_type": "reverse",
"total_length": 52,
"trace_id": "ef459501-7389-453b-b382-42aa714d9e09"
},
"question": "[DYCK LANGUAGE TASK]\n\nINPUT: ⟩{}⦃⦄⟩()⟦⟧])[]⟧⦃⦄⟨⟩>⦆⟩>)}⟧⦅⦆}⦄<>]>>\nDIRECTION: reverse (prepend opening brackets)\n\nCONSTRAINTS:\n- Minimize added brackets\n- Result must be valid Dyck word\n- Preserve input as suffix\n\nPlease provide your final answer in backticks like `answer`."
},
"metadata": {
"fill_length": 17,
"full_sequence": "<<[⦃{⟦{(<⟨⦅<⟦([⟨⟨⟩{}⦃⦄⟩()⟦⟧])[]⟧⦃⦄⟨⟩>⦆⟩>)}⟧⦅⦆}⦄<>]>>",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "<<[⦃{⟦{(<⟨⦅<⟦([⟨⟨",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 65948859,
"suffix_sequence": "⟩{}⦃⦄⟩()⟦⟧])[]⟧⦃⦄⟨⟩>⦆⟩>)}⟧⦅⦆}⦄<>]>>",
"task_type": "reverse",
"total_length": 52,
"trace_id": "ef459501-7389-453b-b382-42aa714d9e09"
},
"seed": 65948859,
"task_id": 465948859,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "⦄{}<>" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⦄{}<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 1,
"full_sequence": "⦃⦄{}<>",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 75743647,
"suffix_sequence": "⦄{}<>",
"task_type": "reverse",
"total_length": 6,
"trace_id": "6749eb25-f9e2-44ec-b8ff-192f248c084b"
},
"question": "Let S = \"⦄{}<>\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 1,
"full_sequence": "⦃⦄{}<>",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 75743647,
"suffix_sequence": "⦄{}<>",
"task_type": "reverse",
"total_length": 6,
"trace_id": "6749eb25-f9e2-44ec-b8ff-192f248c084b"
},
"seed": 75743647,
"task_id": 475743647,
"task_type": "dyck_language2"
} |
logic-v2 | Q: What opening brackets should precede ")>⟩⟩)⟩>)]}}>⟩>}" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{<⟨<{{[(<⟨(⟨⟨<()>⟩⟩)⟩>)]}}>⟩>}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "{<⟨<{{[(<⟨(⟨⟨<()>⟩⟩)⟩>)]}}>⟩>}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{<⟨<{{[(<⟨(⟨⟨<(",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 83187948,
"suffix_sequence": ")>⟩⟩)⟩>)]}}>⟩>}",
"task_type": "reverse",
"total_length": 30,
"trace_id": "8f94db63-2c68-473c-90bb-6da925758c2b"
},
"question": "Q: What opening brackets should precede \")>⟩⟩)⟩>)]}}>⟩>}\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 15,
"full_sequence": "{<⟨<{{[(<⟨(⟨⟨<()>⟩⟩)⟩>)]}}>⟩>}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{<⟨<{{[(<⟨(⟨⟨<(",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 83187948,
"suffix_sequence": ")>⟩⟩)⟩>)]}}>⟩>}",
"task_type": "reverse",
"total_length": 30,
"trace_id": "8f94db63-2c68-473c-90bb-6da925758c2b"
},
"seed": 83187948,
"task_id": 483187948,
"task_type": "dyck_language2"
} |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: [][][]])}}⟨⟩⟨⟩<>{}
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{{([[][][]])}}⟨⟩⟨⟩<>{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "{{([[][][]])}}⟨⟩⟨⟩<>{}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{{([",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 34909544,
"suffix_sequence": "[][][]])}}⟨⟩⟨⟩<>{}",
"task_type": "reverse",
"total_length": 22,
"trace_id": "40f892d5-4a0d-43a1-8a4e-7ce4af65c4e9"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: [][][]])}}⟨⟩⟨⟩<>{}\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 4,
"full_sequence": "{{([[][][]])}}⟨⟩⟨⟩<>{}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{{([",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 34909544,
"suffix_sequence": "[][][]])}}⟨⟩⟨⟩<>{}",
"task_type": "reverse",
"total_length": 22,
"trace_id": "40f892d5-4a0d-43a1-8a4e-7ce4af65c4e9"
},
"seed": 34909544,
"task_id": 434909544,
"task_type": "dyck_language2"
} |
logic-v2 | Fill in the blank:
_____ + []}>>)>()[]]<>[]<>(){}<>[] = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[<(<<{[]}>>)>()[]]<>[]<>(){}<>[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "[<(<<{[]}>>)>()[]]<>[]<>(){}<>[]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<(<<{",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 33399554,
"suffix_sequence": "[]}>>)>()[]]<>[]<>(){}<>[]",
"task_type": "reverse",
"total_length": 32,
"trace_id": "46e8f001-4d46-4a67-9cd9-071d3808962d"
},
"question": "Fill in the blank:\n\n_____ + []}>>)>()[]]<>[]<>(){}<>[] = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 6,
"full_sequence": "[<(<<{[]}>>)>()[]]<>[]<>(){}<>[]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<(<<{",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 33399554,
"suffix_sequence": "[]}>>)>()[]]<>[]<>(){}<>[]",
"task_type": "reverse",
"total_length": 32,
"trace_id": "46e8f001-4d46-4a67-9cd9-071d3808962d"
},
"seed": 33399554,
"task_id": 433399554,
"task_type": "dyck_language2"
} |
logic-v2 | Q: What opening brackets should precede "}⦆⦆⦆⦄⦄}⟩⦄⦆)⟩⟧⦄⦄" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⦃⟦⟨(⦅⦃⟨{⦃⦃⦅⦅⦅{}⦆⦆⦆⦄⦄}⟩⦄⦆)⟩⟧⦄⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "⦃⦃⟦⟨(⦅⦃⟨{⦃⦃⦅⦅⦅{}⦆⦆⦆⦄⦄}⟩⦄⦆)⟩⟧⦄⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦃⦃⟦⟨(⦅⦃⟨{⦃⦃⦅⦅⦅{",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 28989992,
"suffix_sequence": "}⦆⦆⦆⦄⦄}⟩⦄⦆)⟩⟧⦄⦄",
"task_type": "reverse",
"total_length": 30,
"trace_id": "50b24e34-bfe5-4f99-a7dc-203ffaf2880d"
},
"question": "Q: What opening brackets should precede \"}⦆⦆⦆⦄⦄}⟩⦄⦆)⟩⟧⦄⦄\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 15,
"full_sequence": "⦃⦃⟦⟨(⦅⦃⟨{⦃⦃⦅⦅⦅{}⦆⦆⦆⦄⦄}⟩⦄⦆)⟩⟧⦄⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦃⦃⟦⟨(⦅⦃⟨{⦃⦃⦅⦅⦅{",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 28989992,
"suffix_sequence": "}⦆⦆⦆⦄⦄}⟩⦄⦆)⟩⟧⦄⦄",
"task_type": "reverse",
"total_length": 30,
"trace_id": "50b24e34-bfe5-4f99-a7dc-203ffaf2880d"
},
"seed": 28989992,
"task_id": 428989992,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "⦄)}⟨⟩⟧⟩]⟩" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⟨[⟨⟦{(⦃⦄)}⟨⟩⟧⟩]⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "⟨[⟨⟦{(⦃⦄)}⟨⟩⟧⟩]⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[⟨⟦{(⦃",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 54359740,
"suffix_sequence": "⦄)}⟨⟩⟧⟩]⟩",
"task_type": "reverse",
"total_length": 16,
"trace_id": "48dd8810-bcc1-467d-9d73-bc877fa94045"
},
"question": "Let S = \"⦄)}⟨⟩⟧⟩]⟩\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 7,
"full_sequence": "⟨[⟨⟦{(⦃⦄)}⟨⟩⟧⟩]⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨[⟨⟦{(⦃",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 54359740,
"suffix_sequence": "⦄)}⟨⟩⟧⟩]⟩",
"task_type": "reverse",
"total_length": 16,
"trace_id": "48dd8810-bcc1-467d-9d73-bc877fa94045"
},
"seed": 54359740,
"task_id": 454359740,
"task_type": "dyck_language2"
} |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: <>⟨⟩][]{}]][]]}
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{[[[[<>⟨⟩][]{}]][]]}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "{[[[[<>⟨⟩][]{}]][]]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[[[[",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 53435579,
"suffix_sequence": "<>⟨⟩][]{}]][]]}",
"task_type": "reverse",
"total_length": 20,
"trace_id": "f6ce3cc7-d0bc-4390-aefb-6275c3ae686a"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: <>⟨⟩][]{}]][]]}\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 5,
"full_sequence": "{[[[[<>⟨⟩][]{}]][]]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[[[[",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 53435579,
"suffix_sequence": "<>⟨⟩][]{}]][]]}",
"task_type": "reverse",
"total_length": 20,
"trace_id": "f6ce3cc7-d0bc-4390-aefb-6275c3ae686a"
},
"seed": 53435579,
"task_id": 453435579,
"task_type": "dyck_language2"
} |
logic-v2 | Fill in the blank:
_____ + })]]>>]} = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{[<<[[({})]]>>]}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 8,
"full_sequence": "{[<<[[({})]]>>]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[<<[[({",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 78381201,
"suffix_sequence": "})]]>>]}",
"task_type": "reverse",
"total_length": 16,
"trace_id": "9d5f83a5-a9de-466d-8abb-cb9abe8084b6"
},
"question": "Fill in the blank:\n\n_____ + })]]>>]} = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 8,
"full_sequence": "{[<<[[({})]]>>]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{[<<[[({",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 78381201,
"suffix_sequence": "})]]>>]}",
"task_type": "reverse",
"total_length": 16,
"trace_id": "9d5f83a5-a9de-466d-8abb-cb9abe8084b6"
},
"seed": 78381201,
"task_id": 478381201,
"task_type": "dyck_language2"
} |
logic-v2 | Fill in the blank:
_____ + }>>>}}{}⟨⟩[])⟨⟩⟩>>})⟩>⟩⟩} = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{⟨⟨<⟨({<<⟨({{<<<{}>>>}}{}⟨⟩[])⟨⟩⟩>>})⟩>⟩⟩}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "{⟨⟨<⟨({<<⟨({{<<<{}>>>}}{}⟨⟩[])⟨⟩⟩>>})⟩>⟩⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨⟨<⟨({<<⟨({{<<<{",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 26547054,
"suffix_sequence": "}>>>}}{}⟨⟩[])⟨⟩⟩>>})⟩>⟩⟩}",
"task_type": "reverse",
"total_length": 42,
"trace_id": "425633d3-6082-402b-bdea-2236579e89e0"
},
"question": "Fill in the blank:\n\n_____ + }>>>}}{}⟨⟩[])⟨⟩⟩>>})⟩>⟩⟩} = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 17,
"full_sequence": "{⟨⟨<⟨({<<⟨({{<<<{}>>>}}{}⟨⟩[])⟨⟩⟩>>})⟩>⟩⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨⟨<⟨({<<⟨({{<<<{",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 26547054,
"suffix_sequence": "}>>>}}{}⟨⟩[])⟨⟩⟩>>})⟩>⟩⟩}",
"task_type": "reverse",
"total_length": 42,
"trace_id": "425633d3-6082-402b-bdea-2236579e89e0"
},
"seed": 26547054,
"task_id": 426547054,
"task_type": "dyck_language2"
} |
logic-v2 | Fill in the blank:
_____ + }]{}})}()){})})]]]) = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "([[[({(({({[{}]{}})}()){})})]]])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "([[[({(({({[{}]{}})}()){})})]]])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([[[({(({({[{",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 13046608,
"suffix_sequence": "}]{}})}()){})})]]])",
"task_type": "reverse",
"total_length": 32,
"trace_id": "380c0aa5-913e-4d5c-b622-13f48c1339a7"
},
"question": "Fill in the blank:\n\n_____ + }]{}})}()){})})]]]) = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 13,
"full_sequence": "([[[({(({({[{}]{}})}()){})})]]])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([[[({(({({[{",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 13046608,
"suffix_sequence": "}]{}})}()){})})]]])",
"task_type": "reverse",
"total_length": 32,
"trace_id": "380c0aa5-913e-4d5c-b622-13f48c1339a7"
},
"seed": 13046608,
"task_id": 413046608,
"task_type": "dyck_language2"
} |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: []))){}[]])[]{}{}{}{}
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pairs beyond what is required
Please provide your final answer (the complete valid sequence) in backticks like `answer`. | {
"game_data": {
"answer": "([((([]))){}[]])[]{}{}{}{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "([((([]))){}[]])[]{}{}{}{}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([(((",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 10696080,
"suffix_sequence": "[]))){}[]])[]{}{}{}{}",
"task_type": "reverse",
"total_length": 26,
"trace_id": "503aa6b6-2d46-470e-9c44-9a28014de2f4"
},
"question": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: []))){}[]])[]{}{}{}{}\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do not add any extra bracket pairs beyond what is required\n\nPlease provide your final answer (the complete valid sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 5,
"full_sequence": "([((([]))){}[]])[]{}{}{}{}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([(((",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 10696080,
"suffix_sequence": "[]))){}[]])[]{}{}{}{}",
"task_type": "reverse",
"total_length": 26,
"trace_id": "503aa6b6-2d46-470e-9c44-9a28014de2f4"
},
"seed": 10696080,
"task_id": 410696080,
"task_type": "dyck_language2"
} |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: )])]}}))))}])
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "([{(((({{[([()])]}}))))}])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "([{(((({{[([()])]}}))))}])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{(((({{[([(",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 50433179,
"suffix_sequence": ")])]}}))))}])",
"task_type": "reverse",
"total_length": 26,
"trace_id": "636f67ff-c983-49a9-853c-7bd1d6b55e5c"
},
"question": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: )])]}}))))}])\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease provide your final answer (the complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 13,
"full_sequence": "([{(((({{[([()])]}}))))}])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{(((({{[([(",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 50433179,
"suffix_sequence": ")])]}}))))}])",
"task_type": "reverse",
"total_length": 26,
"trace_id": "636f67ff-c983-49a9-853c-7bd1d6b55e5c"
},
"seed": 50433179,
"task_id": 450433179,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "{}])<>)}}⟧()[]⟨⟩⦃⦄⟨⟩⦄)}⟩⦄>⟩⟩" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟨<⦃⟨{(⦃⟦{{(([{}])<>)}}⟧()[]⟨⟩⦃⦄⟨⟩⦄)}⟩⦄>⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 14,
"full_sequence": "⟨⟨<⦃⟨{(⦃⟦{{(([{}])<>)}}⟧()[]⟨⟩⦃⦄⟨⟩⦄)}⟩⦄>⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟨<⦃⟨{(⦃⟦{{(([",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 79580109,
"suffix_sequence": "{}])<>)}}⟧()[]⟨⟩⦃⦄⟨⟩⦄)}⟩⦄>⟩⟩",
"task_type": "reverse",
"total_length": 42,
"trace_id": "ca96eff9-05ee-417d-8fad-1e42b36ee5e5"
},
"question": "Let S = \"{}])<>)}}⟧()[]⟨⟩⦃⦄⟨⟩⦄)}⟩⦄>⟩⟩\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 14,
"full_sequence": "⟨⟨<⦃⟨{(⦃⟦{{(([{}])<>)}}⟧()[]⟨⟩⦃⦄⟨⟩⦄)}⟩⦄>⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟨<⦃⟨{(⦃⟦{{(([",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 79580109,
"suffix_sequence": "{}])<>)}}⟧()[]⟨⟩⦃⦄⟨⟩⦄)}⟩⦄>⟩⟩",
"task_type": "reverse",
"total_length": 42,
"trace_id": "ca96eff9-05ee-417d-8fad-1e42b36ee5e5"
},
"seed": 79580109,
"task_id": 479580109,
"task_type": "dyck_language2"
} |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: {}><>><><>>)}}]}>]>>]
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[<<[<{[{{(<<<{}><>><><>>)}}]}>]>>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "[<<[<{[{{(<<<{}><>><><>>)}}]}>]>>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<<[<{[{{(<<<",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 78101844,
"suffix_sequence": "{}><>><><>>)}}]}>]>>]",
"task_type": "reverse",
"total_length": 34,
"trace_id": "483fcad6-21e9-411f-87c3-3f79b71a44a7"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: {}><>><><>>)}}]}>]>>]\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 13,
"full_sequence": "[<<[<{[{{(<<<{}><>><><>>)}}]}>]>>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<<[<{[{{(<<<",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 78101844,
"suffix_sequence": "{}><>><><>>)}}]}>]>>]",
"task_type": "reverse",
"total_length": 34,
"trace_id": "483fcad6-21e9-411f-87c3-3f79b71a44a7"
},
"seed": 78101844,
"task_id": 478101844,
"task_type": "dyck_language2"
} |
logic-v2 | Q: What opening brackets should precede "⟩]⦃⦄{}>()⟧{}}>⦄⟦⟧{}])⦄>>⟩⟩" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟨<<⦃([⦃<{⟦<[⟨⟩]⦃⦄{}>()⟧{}}>⦄⟦⟧{}])⦄>>⟩⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 14,
"full_sequence": "⟨⟨<<⦃([⦃<{⟦<[⟨⟩]⦃⦄{}>()⟧{}}>⦄⟦⟧{}])⦄>>⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟨<<⦃([⦃<{⟦<[⟨",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 58886791,
"suffix_sequence": "⟩]⦃⦄{}>()⟧{}}>⦄⟦⟧{}])⦄>>⟩⟩",
"task_type": "reverse",
"total_length": 40,
"trace_id": "f831d351-496b-4598-a0ef-996d7bdcd68c"
},
"question": "Q: What opening brackets should precede \"⟩]⦃⦄{}>()⟧{}}>⦄⟦⟧{}])⦄>>⟩⟩\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 14,
"full_sequence": "⟨⟨<<⦃([⦃<{⟦<[⟨⟩]⦃⦄{}>()⟧{}}>⦄⟦⟧{}])⦄>>⟩⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟨<<⦃([⦃<{⟦<[⟨",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 58886791,
"suffix_sequence": "⟩]⦃⦄{}>()⟧{}}>⦄⟦⟧{}])⦄>>⟩⟩",
"task_type": "reverse",
"total_length": 40,
"trace_id": "f831d351-496b-4598-a0ef-996d7bdcd68c"
},
"seed": 58886791,
"task_id": 458886791,
"task_type": "dyck_language2"
} |
logic-v2 | Fill in the blank:
_____ + [][]>})⟩⟩⟩}}⟧⟩⟧⟧}⦄⟩⟧>)>>⟧⟩ = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⟦<<(<⟦⟨⦃{⟦⟦⟨⟦{{⟨⟨⟨({<[][]>})⟩⟩⟩}}⟧⟩⟧⟧}⦄⟩⟧>)>>⟧⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 22,
"full_sequence": "⟨⟦<<(<⟦⟨⦃{⟦⟦⟨⟦{{⟨⟨⟨({<[][]>})⟩⟩⟩}}⟧⟩⟧⟧}⦄⟩⟧>)>>⟧⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟦<<(<⟦⟨⦃{⟦⟦⟨⟦{{⟨⟨⟨({<",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 24180932,
"suffix_sequence": "[][]>})⟩⟩⟩}}⟧⟩⟧⟧}⦄⟩⟧>)>>⟧⟩",
"task_type": "reverse",
"total_length": 48,
"trace_id": "cb36c0fb-d9dd-4026-a24b-c00d98908940"
},
"question": "Fill in the blank:\n\n_____ + [][]>})⟩⟩⟩}}⟧⟩⟧⟧}⦄⟩⟧>)>>⟧⟩ = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 22,
"full_sequence": "⟨⟦<<(<⟦⟨⦃{⟦⟦⟨⟦{{⟨⟨⟨({<[][]>})⟩⟩⟩}}⟧⟩⟧⟧}⦄⟩⟧>)>>⟧⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⟦<<(<⟦⟨⦃{⟦⟦⟨⟦{{⟨⟨⟨({<",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 24180932,
"suffix_sequence": "[][]>})⟩⟩⟩}}⟧⟩⟧⟧}⦄⟩⟧>)>>⟧⟩",
"task_type": "reverse",
"total_length": 48,
"trace_id": "cb36c0fb-d9dd-4026-a24b-c00d98908940"
},
"seed": 24180932,
"task_id": 424180932,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"})[]>"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<({})[]>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "<({})[]>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<({",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 6920077,
"suffix_sequence": "})[]>",
"task_type": "reverse",
"total_length": 8,
"trace_id": "016829f2-0137-4f87-a1ea-46db34fd734d"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\"})[]>\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 3,
"full_sequence": "<({})[]>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<({",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 6920077,
"suffix_sequence": "})[]>",
"task_type": "reverse",
"total_length": 8,
"trace_id": "016829f2-0137-4f87-a1ea-46db34fd734d"
},
"seed": 6920077,
"task_id": 406920077,
"task_type": "dyck_language2"
} |
logic-v2 | Fill in the blank:
_____ + )]]]()])]]}]) = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "([{[[([[[[()]]]()])]]}])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "([{[[([[[[()]]]()])]]}])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{[[([[[[(",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 64469239,
"suffix_sequence": ")]]]()])]]}])",
"task_type": "reverse",
"total_length": 24,
"trace_id": "27041c15-f6aa-46c2-bce8-3638ddefc57e"
},
"question": "Fill in the blank:\n\n_____ + )]]]()])]]}]) = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 11,
"full_sequence": "([{[[([[[[()]]]()])]]}])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{[[([[[[(",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 64469239,
"suffix_sequence": ")]]]()])]]}])",
"task_type": "reverse",
"total_length": 24,
"trace_id": "27041c15-f6aa-46c2-bce8-3638ddefc57e"
},
"seed": 64469239,
"task_id": 464469239,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "⟦⟧>⟦⟧⟦⟧⦄⦆<>⟧⦄{}⟩{}⟨⟩<>⦄)[]()⦃⦄⟦⟧]⟨⟩⟧())⦃⦄{}()<>" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "(⟦[(⦃⟨⦃⟦⦅⦃<⟦⟧>⟦⟧⟦⟧⦄⦆<>⟧⦄{}⟩{}⟨⟩<>⦄)[]()⦃⦄⟦⟧]⟨⟩⟧())⦃⦄{}()<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "(⟦[(⦃⟨⦃⟦⦅⦃<⟦⟧>⟦⟧⟦⟧⦄⦆<>⟧⦄{}⟩{}⟨⟩<>⦄)[]()⦃⦄⟦⟧]⟨⟩⟧())⦃⦄{}()<>",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "(⟦[(⦃⟨⦃⟦⦅⦃<",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 2055420,
"suffix_sequence": "⟦⟧>⟦⟧⟦⟧⦄⦆<>⟧⦄{}⟩{}⟨⟩<>⦄)[]()⦃⦄⟦⟧]⟨⟩⟧())⦃⦄{}()<>",
"task_type": "reverse",
"total_length": 58,
"trace_id": "f7c8d38c-9e57-4f68-9afe-97ad078def63"
},
"question": "Let S = \"⟦⟧>⟦⟧⟦⟧⦄⦆<>⟧⦄{}⟩{}⟨⟩<>⦄)[]()⦃⦄⟦⟧]⟨⟩⟧())⦃⦄{}()<>\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 11,
"full_sequence": "(⟦[(⦃⟨⦃⟦⦅⦃<⟦⟧>⟦⟧⟦⟧⦄⦆<>⟧⦄{}⟩{}⟨⟩<>⦄)[]()⦃⦄⟦⟧]⟨⟩⟧())⦃⦄{}()<>",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "(⟦[(⦃⟨⦃⟦⦅⦃<",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 2055420,
"suffix_sequence": "⟦⟧>⟦⟧⟦⟧⦄⦆<>⟧⦄{}⟩{}⟨⟩<>⦄)[]()⦃⦄⟦⟧]⟨⟩⟧())⦃⦄{}()<>",
"task_type": "reverse",
"total_length": 58,
"trace_id": "f7c8d38c-9e57-4f68-9afe-97ad078def63"
},
"seed": 2055420,
"task_id": 402055420,
"task_type": "dyck_language2"
} |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ⦅⦆⦄)[]>{}⦆⟩⟧[]}]⟩})⟩>)}>⟩⦄⦆}⟧
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟦{⦅⦃⟨<{(<⟨({⟨[{⟦⟨⦅<(⦃⦅⦆⦄)[]>{}⦆⟩⟧[]}]⟩})⟩>)}>⟩⦄⦆}⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 21,
"full_sequence": "⟦{⦅⦃⟨<{(<⟨({⟨[{⟦⟨⦅<(⦃⦅⦆⦄)[]>{}⦆⟩⟧[]}]⟩})⟩>)}>⟩⦄⦆}⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟦{⦅⦃⟨<{(<⟨({⟨[{⟦⟨⦅<(⦃",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 10562120,
"suffix_sequence": "⦅⦆⦄)[]>{}⦆⟩⟧[]}]⟩})⟩>)}>⟩⦄⦆}⟧",
"task_type": "reverse",
"total_length": 50,
"trace_id": "e1941a8d-aa65-4007-a4f3-367353ecc631"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ⦅⦆⦄)[]>{}⦆⟩⟧[]}]⟩})⟩>)}>⟩⦄⦆}⟧\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 21,
"full_sequence": "⟦{⦅⦃⟨<{(<⟨({⟨[{⟦⟨⦅<(⦃⦅⦆⦄)[]>{}⦆⟩⟧[]}]⟩})⟩>)}>⟩⦄⦆}⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟦{⦅⦃⟨<{(<⟨({⟨[{⟦⟨⦅<(⦃",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 10562120,
"suffix_sequence": "⦅⦆⦄)[]>{}⦆⟩⟧[]}]⟩})⟩>)}>⟩⦄⦆}⟧",
"task_type": "reverse",
"total_length": 50,
"trace_id": "e1941a8d-aa65-4007-a4f3-367353ecc631"
},
"seed": 10562120,
"task_id": 410562120,
"task_type": "dyck_language2"
} |
logic-v2 | Fill in the blank:
_____ + }()⟩()<><>⦃⦄⟧⟩<>]⟩]⟧⟩}⦆⦆⦄ = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⦅⦅{⟨⟦[⟨[⟨⟦⟨{}()⟩()<><>⦃⦄⟧⟩<>]⟩]⟧⟩}⦆⦆⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "⦃⦅⦅{⟨⟦[⟨[⟨⟦⟨{}()⟩()<><>⦃⦄⟧⟩<>]⟩]⟧⟩}⦆⦆⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦃⦅⦅{⟨⟦[⟨[⟨⟦⟨{",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 81331451,
"suffix_sequence": "}()⟩()<><>⦃⦄⟧⟩<>]⟩]⟧⟩}⦆⦆⦄",
"task_type": "reverse",
"total_length": 38,
"trace_id": "ce60629a-6b4d-4b6d-b141-aab131226a5f"
},
"question": "Fill in the blank:\n\n_____ + }()⟩()<><>⦃⦄⟧⟩<>]⟩]⟧⟩}⦆⦆⦄ = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 13,
"full_sequence": "⦃⦅⦅{⟨⟦[⟨[⟨⟦⟨{}()⟩()<><>⦃⦄⟧⟩<>]⟩]⟧⟩}⦆⦆⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⦃⦅⦅{⟨⟦[⟨[⟨⟦⟨{",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 81331451,
"suffix_sequence": "}()⟩()<><>⦃⦄⟧⟩<>]⟩]⟧⟩}⦆⦆⦄",
"task_type": "reverse",
"total_length": 38,
"trace_id": "ce60629a-6b4d-4b6d-b141-aab131226a5f"
},
"seed": 81331451,
"task_id": 481331451,
"task_type": "dyck_language2"
} |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: []>){})[][]}]<>[]
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pairs beyond what is required
Please provide your final answer (the complete valid sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[{((<[]>){})[][]}]<>[]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "[{((<[]>){})[][]}]<>[]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{((<",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 9384009,
"suffix_sequence": "[]>){})[][]}]<>[]",
"task_type": "reverse",
"total_length": 22,
"trace_id": "9ab4d46e-1279-4c32-8ba1-233da23ab076"
},
"question": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: []>){})[][]}]<>[]\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do not add any extra bracket pairs beyond what is required\n\nPlease provide your final answer (the complete valid sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 5,
"full_sequence": "[{((<[]>){})[][]}]<>[]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{((<",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 9384009,
"suffix_sequence": "[]>){})[][]}]<>[]",
"task_type": "reverse",
"total_length": 22,
"trace_id": "9ab4d46e-1279-4c32-8ba1-233da23ab076"
},
"seed": 9384009,
"task_id": 409384009,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"}{})⟧⟧}}]⟨⟩{}[]]>]⟩}⟩⟩>"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<⟨⟨{⟨[<[[{{⟦⟦({}{})⟧⟧}}]⟨⟩{}[]]>]⟩}⟩⟩>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "<⟨⟨{⟨[<[[{{⟦⟦({}{})⟧⟧}}]⟨⟩{}[]]>]⟩}⟩⟩>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟨⟨{⟨[<[[{{⟦⟦({",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 43550172,
"suffix_sequence": "}{})⟧⟧}}]⟨⟩{}[]]>]⟩}⟩⟩>",
"task_type": "reverse",
"total_length": 38,
"trace_id": "7dc14e5e-2606-4027-beee-558d8c204f26"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\"}{})⟧⟧}}]⟨⟩{}[]]>]⟩}⟩⟩>\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 15,
"full_sequence": "<⟨⟨{⟨[<[[{{⟦⟦({}{})⟧⟧}}]⟨⟩{}[]]>]⟩}⟩⟩>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟨⟨{⟨[<[[{{⟦⟦({",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 43550172,
"suffix_sequence": "}{})⟧⟧}}]⟨⟩{}[]]>]⟩}⟩⟩>",
"task_type": "reverse",
"total_length": 38,
"trace_id": "7dc14e5e-2606-4027-beee-558d8c204f26"
},
"seed": 43550172,
"task_id": 443550172,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "⟦⟧}⟧[]}{}<>()))⟧))))]>]}⟩⟩>" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "<⟨⟨{[<[((((⟦(({⟦{⟦⟧}⟧[]}{}<>()))⟧))))]>]}⟩⟩>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "<⟨⟨{[<[((((⟦(({⟦{⟦⟧}⟧[]}{}<>()))⟧))))]>]}⟩⟩>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟨⟨{[<[((((⟦(({⟦{",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 71655523,
"suffix_sequence": "⟦⟧}⟧[]}{}<>()))⟧))))]>]}⟩⟩>",
"task_type": "reverse",
"total_length": 44,
"trace_id": "a5b91fb4-9c90-41c6-8272-0a20ff39a275"
},
"question": "Let S = \"⟦⟧}⟧[]}{}<>()))⟧))))]>]}⟩⟩>\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 17,
"full_sequence": "<⟨⟨{[<[((((⟦(({⟦{⟦⟧}⟧[]}{}<>()))⟧))))]>]}⟩⟩>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟨⟨{[<[((((⟦(({⟦{",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 71655523,
"suffix_sequence": "⟦⟧}⟧[]}{}<>()))⟧))))]>]}⟩⟩>",
"task_type": "reverse",
"total_length": 44,
"trace_id": "a5b91fb4-9c90-41c6-8272-0a20ff39a275"
},
"seed": 71655523,
"task_id": 471655523,
"task_type": "dyck_language2"
} |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: >>])}[]}>)}<>{}>](){}{}>})>}>)]}]
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "[{[(<{<({<[<{(<{{([<<>>])}[]}>)}<>{}>](){}{}>})>}>)]}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 21,
"full_sequence": "[{[(<{<({<[<{(<{{([<<>>])}[]}>)}<>{}>](){}{}>})>}>)]}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{[(<{<({<[<{(<{{([<<",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 2585810,
"suffix_sequence": ">>])}[]}>)}<>{}>](){}{}>})>}>)]}]",
"task_type": "reverse",
"total_length": 54,
"trace_id": "287e1448-a426-4cba-88f8-4c2b7f281e1e"
},
"question": "[DYCK LANGUAGE TASK]\n\nINPUT: >>])}[]}>)}<>{}>](){}{}>})>}>)]}]\nDIRECTION: reverse (prepend opening brackets)\n\nCONSTRAINTS:\n- Minimize added brackets\n- Result must be valid Dyck word\n- Preserve input as suffix\n\nPlease provide your final answer in backticks like `answer`."
},
"metadata": {
"fill_length": 21,
"full_sequence": "[{[(<{<({<[<{(<{{([<<>>])}[]}>)}<>{}>](){}{}>})>}>)]}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{[(<{<({<[<{(<{{([<<",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 2585810,
"suffix_sequence": ">>])}[]}>)}<>{}>](){}{}>})>}>)]}]",
"task_type": "reverse",
"total_length": 54,
"trace_id": "287e1448-a426-4cba-88f8-4c2b7f281e1e"
},
"seed": 2585810,
"task_id": 402585810,
"task_type": "dyck_language2"
} |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: <>)⟩))⟩⟦⟧)<>)⟧[]⟧⟩⟧<>⟧[]>⟦⟧[]()⟨⟩<>⟨⟩
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pairs beyond what is required
Please provide your final answer (the complete valid sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<⟦⟦⟨⟦⟦((⟨((⟨(<>)⟩))⟩⟦⟧)<>)⟧[]⟧⟩⟧<>⟧[]>⟦⟧[]()⟨⟩<>⟨⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "<⟦⟦⟨⟦⟦((⟨((⟨(<>)⟩))⟩⟦⟧)<>)⟧[]⟧⟩⟧<>⟧[]>⟦⟧[]()⟨⟩<>⟨⟩",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟦⟦⟨⟦⟦((⟨((⟨(",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 78220808,
"suffix_sequence": "<>)⟩))⟩⟦⟧)<>)⟧[]⟧⟩⟧<>⟧[]>⟦⟧[]()⟨⟩<>⟨⟩",
"task_type": "reverse",
"total_length": 50,
"trace_id": "32c7a0bc-0905-4943-a009-aaa08f12e5b4"
},
"question": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: <>)⟩))⟩⟦⟧)<>)⟧[]⟧⟩⟧<>⟧[]>⟦⟧[]()⟨⟩<>⟨⟩\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do not add any extra bracket pairs beyond what is required\n\nPlease provide your final answer (the complete valid sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 13,
"full_sequence": "<⟦⟦⟨⟦⟦((⟨((⟨(<>)⟩))⟩⟦⟧)<>)⟧[]⟧⟩⟧<>⟧[]>⟦⟧[]()⟨⟩<>⟨⟩",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟦⟦⟨⟦⟦((⟨((⟨(",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 78220808,
"suffix_sequence": "<>)⟩))⟩⟦⟧)<>)⟧[]⟧⟩⟧<>⟧[]>⟦⟧[]()⟨⟩<>⟨⟩",
"task_type": "reverse",
"total_length": 50,
"trace_id": "32c7a0bc-0905-4943-a009-aaa08f12e5b4"
},
"seed": 78220808,
"task_id": 478220808,
"task_type": "dyck_language2"
} |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ]]>)}
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "{(<[[]]>)}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "{(<[[]]>)}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{(<[[",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 19497510,
"suffix_sequence": "]]>)}",
"task_type": "reverse",
"total_length": 10,
"trace_id": "7a4e6482-b2ab-4547-9d43-db596be8a226"
},
"question": "[DYCK LANGUAGE TASK]\n\nINPUT: ]]>)}\nDIRECTION: reverse (prepend opening brackets)\n\nCONSTRAINTS:\n- Minimize added brackets\n- Result must be valid Dyck word\n- Preserve input as suffix\n\nPlease provide your final answer in backticks like `answer`."
},
"metadata": {
"fill_length": 5,
"full_sequence": "{(<[[]]>)}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{(<[[",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 19497510,
"suffix_sequence": "]]>)}",
"task_type": "reverse",
"total_length": 10,
"trace_id": "7a4e6482-b2ab-4547-9d43-db596be8a226"
},
"seed": 19497510,
"task_id": 419497510,
"task_type": "dyck_language2"
} |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: )[]}}()()[][])}()]{}}{}()](){}{}]}]]]])))
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pairs beyond what is required
Please provide your final answer (the complete valid sequence) in backticks like `answer`. | {
"game_data": {
"answer": "((([[[[{[[{[{({{()[]}}()()[][])}()]{}}{}()](){}{}]}]]]])))",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "((([[[[{[[{[{({{()[]}}()()[][])}()]{}}{}()](){}{}]}]]]])))",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "((([[[[{[[{[{({{(",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 72882638,
"suffix_sequence": ")[]}}()()[][])}()]{}}{}()](){}{}]}]]]])))",
"task_type": "reverse",
"total_length": 58,
"trace_id": "3d0f1edd-89a1-4a77-b0f0-98a21a63e4d2"
},
"question": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: )[]}}()()[][])}()]{}}{}()](){}{}]}]]]])))\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do not add any extra bracket pairs beyond what is required\n\nPlease provide your final answer (the complete valid sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 17,
"full_sequence": "((([[[[{[[{[{({{()[]}}()()[][])}()]{}}{}()](){}{}]}]]]])))",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "((([[[[{[[{[{({{(",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 72882638,
"suffix_sequence": ")[]}}()()[][])}()]{}}{}()](){}{}]}]]]])))",
"task_type": "reverse",
"total_length": 58,
"trace_id": "3d0f1edd-89a1-4a77-b0f0-98a21a63e4d2"
},
"seed": 72882638,
"task_id": 472882638,
"task_type": "dyck_language2"
} |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ⦃⦄⟨⟩⟧<>⦆⦆⟦⟧⟧⟩)]⟩⟧
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟦⟨[(⟨⟦⦅⦅⟦⦃⦄⟨⟩⟧<>⦆⦆⟦⟧⟧⟩)]⟩⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "⟦⟨[(⟨⟦⦅⦅⟦⦃⦄⟨⟩⟧<>⦆⦆⟦⟧⟧⟩)]⟩⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟦⟨[(⟨⟦⦅⦅⟦",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 56491712,
"suffix_sequence": "⦃⦄⟨⟩⟧<>⦆⦆⟦⟧⟧⟩)]⟩⟧",
"task_type": "reverse",
"total_length": 26,
"trace_id": "4bdeb52a-e5b8-44ac-9757-d2a24ed81e74"
},
"question": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: ⦃⦄⟨⟩⟧<>⦆⦆⟦⟧⟧⟩)]⟩⟧\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease provide your final answer (the complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 9,
"full_sequence": "⟦⟨[(⟨⟦⦅⦅⟦⦃⦄⟨⟩⟧<>⦆⦆⟦⟧⟧⟩)]⟩⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟦⟨[(⟨⟦⦅⦅⟦",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 56491712,
"suffix_sequence": "⦃⦄⟨⟩⟧<>⦆⦆⟦⟧⟧⟩)]⟩⟧",
"task_type": "reverse",
"total_length": 26,
"trace_id": "4bdeb52a-e5b8-44ac-9757-d2a24ed81e74"
},
"seed": 56491712,
"task_id": 456491712,
"task_type": "dyck_language2"
} |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: []]()
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "[[]]()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 1,
"full_sequence": "[[]]()",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 72482588,
"suffix_sequence": "[]]()",
"task_type": "reverse",
"total_length": 6,
"trace_id": "dfdc07fb-a4af-4e7d-a68d-0b4c3dee1840"
},
"question": "[DYCK LANGUAGE TASK]\n\nINPUT: []]()\nDIRECTION: reverse (prepend opening brackets)\n\nCONSTRAINTS:\n- Minimize added brackets\n- Result must be valid Dyck word\n- Preserve input as suffix\n\nPlease provide your final answer in backticks like `answer`."
},
"metadata": {
"fill_length": 1,
"full_sequence": "[[]]()",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 72482588,
"suffix_sequence": "[]]()",
"task_type": "reverse",
"total_length": 6,
"trace_id": "dfdc07fb-a4af-4e7d-a68d-0b4c3dee1840"
},
"seed": 72482588,
"task_id": 472482588,
"task_type": "dyck_language2"
} |
logic-v2 | Q: What opening brackets should precede "]])<>>}))>>}]" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[{<<(({<([[]])<>>}))>>}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "[{<<(({<([[]])<>>}))>>}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{<<(({<([[",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 1553714,
"suffix_sequence": "]])<>>}))>>}]",
"task_type": "reverse",
"total_length": 24,
"trace_id": "95bca7af-cba0-49bf-97df-384b2c440c45"
},
"question": "Q: What opening brackets should precede \"]])<>>}))>>}]\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 11,
"full_sequence": "[{<<(({<([[]])<>>}))>>}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{<<(({<([[",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 1553714,
"suffix_sequence": "]])<>>}))>>}]",
"task_type": "reverse",
"total_length": 24,
"trace_id": "95bca7af-cba0-49bf-97df-384b2c440c45"
},
"seed": 1553714,
"task_id": 401553714,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "()}{}})[]())]]])()]}{}}[]]){}[]])})" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "({([([{{[([[[(({{()}{}})[]())]]])()]}{}}[]]){}[]])})",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "({([([{{[([[[(({{()}{}})[]())]]])()]}{}}[]]){}[]])})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({([([{{[([[[(({{",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 83595913,
"suffix_sequence": "()}{}})[]())]]])()]}{}}[]]){}[]])})",
"task_type": "reverse",
"total_length": 52,
"trace_id": "ae51a060-d3eb-48ce-ac47-b2b5a1ba172c"
},
"question": "Let S = \"()}{}})[]())]]])()]}{}}[]]){}[]])})\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 17,
"full_sequence": "({([([{{[([[[(({{()}{}})[]())]]])()]}{}}[]]){}[]])})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({([([{{[([[[(({{",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 83595913,
"suffix_sequence": "()}{}})[]())]]])()]}{}}[]]){}[]])})",
"task_type": "reverse",
"total_length": 52,
"trace_id": "ae51a060-d3eb-48ce-ac47-b2b5a1ba172c"
},
"seed": 83595913,
"task_id": 483595913,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "[]()){}<>]" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "[([]()){}<>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 2,
"full_sequence": "[([]()){}<>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[(",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 5585759,
"suffix_sequence": "[]()){}<>]",
"task_type": "reverse",
"total_length": 12,
"trace_id": "17fd155e-2163-4f77-b643-17f500f504d6"
},
"question": "Let S = \"[]()){}<>]\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 2,
"full_sequence": "[([]()){}<>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[(",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 5585759,
"suffix_sequence": "[]()){}<>]",
"task_type": "reverse",
"total_length": 12,
"trace_id": "17fd155e-2163-4f77-b643-17f500f504d6"
},
"seed": 5585759,
"task_id": 405585759,
"task_type": "dyck_language2"
} |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ⦄⦄⦄⦄
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pairs beyond what is required
Please provide your final answer (the complete valid sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⦃⦃⦃⦄⦄⦄⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "⦃⦃⦃⦃⦄⦄⦄⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⦃⦃⦃",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 18229713,
"suffix_sequence": "⦄⦄⦄⦄",
"task_type": "reverse",
"total_length": 8,
"trace_id": "fc3bbbee-c67c-4c5e-be2b-bc818e0a801c"
},
"question": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ⦄⦄⦄⦄\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do not add any extra bracket pairs beyond what is required\n\nPlease provide your final answer (the complete valid sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 4,
"full_sequence": "⦃⦃⦃⦃⦄⦄⦄⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⦃⦃⦃",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 18229713,
"suffix_sequence": "⦄⦄⦄⦄",
"task_type": "reverse",
"total_length": 8,
"trace_id": "fc3bbbee-c67c-4c5e-be2b-bc818e0a801c"
},
"seed": 18229713,
"task_id": 418229713,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"]{}}>{}>)][]}()[]>]{}[]()>]}}>]"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[<{{[<[<{[(<<{[]{}}>{}>)][]}()[]>]{}[]()>]}}>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "[<{{[<[<{[(<<{[]{}}>{}>)][]}()[]>]{}[]()>]}}>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<{{[<[<{[(<<{[",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 24221602,
"suffix_sequence": "]{}}>{}>)][]}()[]>]{}[]()>]}}>]",
"task_type": "reverse",
"total_length": 46,
"trace_id": "7db42709-9f7c-471c-b5fc-450db1eecf15"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\"]{}}>{}>)][]}()[]>]{}[]()>]}}>]\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 15,
"full_sequence": "[<{{[<[<{[(<<{[]{}}>{}>)][]}()[]>]{}[]()>]}}>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<{{[<[<{[(<<{[",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 24221602,
"suffix_sequence": "]{}}>{}>)][]}()[]>]{}[]()>]}}>]",
"task_type": "reverse",
"total_length": 46,
"trace_id": "7db42709-9f7c-471c-b5fc-450db1eecf15"
},
"seed": 24221602,
"task_id": 424221602,
"task_type": "dyck_language2"
} |
logic-v2 | Q: What opening brackets should precede "{}]()})][]{}}}{}(){}}}]}))]}]}})" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "({{[{[(({[{{{{[({[{}]()})][]{}}}{}(){}}}]}))]}]}})",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"full_sequence": "({{[{[(({[{{{{[({[{}]()})][]{}}}{}(){}}}]}))]}]}})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({{[{[(({[{{{{[({[",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 91007366,
"suffix_sequence": "{}]()})][]{}}}{}(){}}}]}))]}]}})",
"task_type": "reverse",
"total_length": 50,
"trace_id": "d704d777-7a30-41cd-91c3-64db276d4cb8"
},
"question": "Q: What opening brackets should precede \"{}]()})][]{}}}{}(){}}}]}))]}]}})\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 18,
"full_sequence": "({{[{[(({[{{{{[({[{}]()})][]{}}}{}(){}}}]}))]}]}})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({{[{[(({[{{{{[({[",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 91007366,
"suffix_sequence": "{}]()})][]{}}}{}(){}}}]}))]}]}})",
"task_type": "reverse",
"total_length": 50,
"trace_id": "d704d777-7a30-41cd-91c3-64db276d4cb8"
},
"seed": 91007366,
"task_id": 491007366,
"task_type": "dyck_language2"
} |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: ⟧⦄]⟨⟩]⟩⦃⦄[]()<>⟦⟧
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨[[⦃⟦⟧⦄]⟨⟩]⟩⦃⦄[]()<>⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "⟨[[⦃⟦⟧⦄]⟨⟩]⟩⦃⦄[]()<>⟦⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟨[[⦃⟦",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 71948999,
"suffix_sequence": "⟧⦄]⟨⟩]⟩⦃⦄[]()<>⟦⟧",
"task_type": "reverse",
"total_length": 22,
"trace_id": "e17c0b85-e322-4937-95cd-13efed10e9c5"
},
"question": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: ⟧⦄]⟨⟩]⟩⦃⦄[]()<>⟦⟧\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease provide your final answer (the complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 5,
"full_sequence": "⟨[[⦃⟦⟧⦄]⟨⟩]⟩⦃⦄[]()<>⟦⟧",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "⟨[[⦃⟦",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 71948999,
"suffix_sequence": "⟧⦄]⟨⟩]⟩⦃⦄[]()<>⟦⟧",
"task_type": "reverse",
"total_length": 22,
"trace_id": "e17c0b85-e322-4937-95cd-13efed10e9c5"
},
"seed": 71948999,
"task_id": 471948999,
"task_type": "dyck_language2"
} |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: [][]]>⟩}<>]>⟩}}⟨⟩})()]>⟩}
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{⟨<[({{{⟨<[{⟨<[[][]]>⟩}<>]>⟩}}⟨⟩})()]>⟩}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "{⟨<[({{{⟨<[{⟨<[[][]]>⟩}<>]>⟩}}⟨⟩})()]>⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨<[({{{⟨<[{⟨<[",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 29125749,
"suffix_sequence": "[][]]>⟩}<>]>⟩}}⟨⟩})()]>⟩}",
"task_type": "reverse",
"total_length": 40,
"trace_id": "5281541c-dc52-4a41-8a4f-f107a19557d3"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: [][]]>⟩}<>]>⟩}}⟨⟩})()]>⟩}\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 15,
"full_sequence": "{⟨<[({{{⟨<[{⟨<[[][]]>⟩}<>]>⟩}}⟨⟩})()]>⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨<[({{{⟨<[{⟨<[",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 29125749,
"suffix_sequence": "[][]]>⟩}<>]>⟩}}⟨⟩})()]>⟩}",
"task_type": "reverse",
"total_length": 40,
"trace_id": "5281541c-dc52-4a41-8a4f-f107a19557d3"
},
"seed": 29125749,
"task_id": 429125749,
"task_type": "dyck_language2"
} |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ])⟧⟦⟧⦄⦄⦃⦄⟧<>()⦄<>()⟧⟩()⦄⦄()⟦⟧()⟦⟧<>⦃⦄()<>
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⦃⟨⟦⦃⟦⦃⦃⟦([])⟧⟦⟧⦄⦄⦃⦄⟧<>()⦄<>()⟧⟩()⦄⦄()⟦⟧()⟦⟧<>⦃⦄()<>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 11,
"full_sequence": "⦃⦃⟨⟦⦃⟦⦃⦃⟦([])⟧⟦⟧⦄⦄⦃⦄⟧<>()⦄<>()⟧⟩()⦄⦄()⟦⟧()⟦⟧<>⦃⦄()<>",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⦃⟨⟦⦃⟦⦃⦃⟦([",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 45054209,
"suffix_sequence": "])⟧⟦⟧⦄⦄⦃⦄⟧<>()⦄<>()⟧⟩()⦄⦄()⟦⟧()⟦⟧<>⦃⦄()<>",
"task_type": "reverse",
"total_length": 52,
"trace_id": "ba24b18d-d96b-4b5e-b11f-552f2f1e1bf0"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ])⟧⟦⟧⦄⦄⦃⦄⟧<>()⦄<>()⟧⟩()⦄⦄()⟦⟧()⟦⟧<>⦃⦄()<>\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 11,
"full_sequence": "⦃⦃⟨⟦⦃⟦⦃⦃⟦([])⟧⟦⟧⦄⦄⦃⦄⟧<>()⦄<>()⟧⟩()⦄⦄()⟦⟧()⟦⟧<>⦃⦄()<>",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⦃⟨⟦⦃⟦⦃⦃⟦([",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 45054209,
"suffix_sequence": "])⟧⟦⟧⦄⦄⦃⦄⟧<>()⦄<>()⟧⟩()⦄⦄()⟦⟧()⟦⟧<>⦃⦄()<>",
"task_type": "reverse",
"total_length": 52,
"trace_id": "ba24b18d-d96b-4b5e-b11f-552f2f1e1bf0"
},
"seed": 45054209,
"task_id": 445054209,
"task_type": "dyck_language2"
} |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ))}}])}))]}})}])
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "([{({{[(({([{{(())}}])}))]}})}])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 16,
"full_sequence": "([{({{[(({([{{(())}}])}))]}})}])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{({{[(({([{{((",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 63635711,
"suffix_sequence": "))}}])}))]}})}])",
"task_type": "reverse",
"total_length": 32,
"trace_id": "c8f4c3df-6896-4dfb-9036-a95cfdb6931f"
},
"question": "[DYCK LANGUAGE TASK]\n\nINPUT: ))}}])}))]}})}])\nDIRECTION: reverse (prepend opening brackets)\n\nCONSTRAINTS:\n- Minimize added brackets\n- Result must be valid Dyck word\n- Preserve input as suffix\n\nPlease provide your final answer in backticks like `answer`."
},
"metadata": {
"fill_length": 16,
"full_sequence": "([{({{[(({([{{(())}}])}))]}})}])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{({{[(({([{{((",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 63635711,
"suffix_sequence": "))}}])}))]}})}])",
"task_type": "reverse",
"total_length": 32,
"trace_id": "c8f4c3df-6896-4dfb-9036-a95cfdb6931f"
},
"seed": 63635711,
"task_id": 463635711,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"[]][]]]))()()"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "(([[[[]][]]]))()()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "(([[[[]][]]]))()()",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(([[[",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 59017462,
"suffix_sequence": "[]][]]]))()()",
"task_type": "reverse",
"total_length": 18,
"trace_id": "7a473981-e47f-4ea2-9d00-f2ad16f8d8d4"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\"[]][]]]))()()\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 5,
"full_sequence": "(([[[[]][]]]))()()",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(([[[",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 59017462,
"suffix_sequence": "[]][]]]))()()",
"task_type": "reverse",
"total_length": 18,
"trace_id": "7a473981-e47f-4ea2-9d00-f2ad16f8d8d4"
},
"seed": 59017462,
"task_id": 459017462,
"task_type": "dyck_language2"
} |
logic-v2 | Q: What opening brackets should precede ")][]{}}()[]}}]]}}]]]}})" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "({{[[[{{[[{{{[()][]{}}()[]}}]]}}]]]}})",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 15,
"full_sequence": "({{[[[{{[[{{{[()][]{}}()[]}}]]}}]]]}})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({{[[[{{[[{{{[(",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 32612970,
"suffix_sequence": ")][]{}}()[]}}]]}}]]]}})",
"task_type": "reverse",
"total_length": 38,
"trace_id": "4294d969-d2ac-411a-8924-975ec9a4e96f"
},
"question": "Q: What opening brackets should precede \")][]{}}()[]}}]]}}]]]}})\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 15,
"full_sequence": "({{[[[{{[[{{{[()][]{}}()[]}}]]}}]]]}})",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({{[[[{{[[{{{[(",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 32612970,
"suffix_sequence": ")][]{}}()[]}}]]}}]]]}})",
"task_type": "reverse",
"total_length": 38,
"trace_id": "4294d969-d2ac-411a-8924-975ec9a4e96f"
},
"seed": 32612970,
"task_id": 432612970,
"task_type": "dyck_language2"
} |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: }⟩⟧⟧{})]⟦⟧⟩]⟦⟧⟧<>>⟦⟧{}[]]))>⟧>
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pairs beyond what is required
Please provide your final answer (the complete valid sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<⟦<(([<⟦[⟨[(⟦⟦⟨{}⟩⟧⟧{})]⟦⟧⟩]⟦⟧⟧<>>⟦⟧{}[]]))>⟧>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 16,
"full_sequence": "<⟦<(([<⟦[⟨[(⟦⟦⟨{}⟩⟧⟧{})]⟦⟧⟩]⟦⟧⟧<>>⟦⟧{}[]]))>⟧>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟦<(([<⟦[⟨[(⟦⟦⟨{",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 7387085,
"suffix_sequence": "}⟩⟧⟧{})]⟦⟧⟩]⟦⟧⟧<>>⟦⟧{}[]]))>⟧>",
"task_type": "reverse",
"total_length": 46,
"trace_id": "9b213fb2-0821-4586-8b73-7ac2859d31e4"
},
"question": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: }⟩⟧⟧{})]⟦⟧⟩]⟦⟧⟧<>>⟦⟧{}[]]))>⟧>\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do not add any extra bracket pairs beyond what is required\n\nPlease provide your final answer (the complete valid sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 16,
"full_sequence": "<⟦<(([<⟦[⟨[(⟦⟦⟨{}⟩⟧⟧{})]⟦⟧⟩]⟦⟧⟧<>>⟦⟧{}[]]))>⟧>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟦<(([<⟦[⟨[(⟦⟦⟨{",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 7387085,
"suffix_sequence": "}⟩⟧⟧{})]⟦⟧⟩]⟦⟧⟧<>>⟦⟧{}[]]))>⟧>",
"task_type": "reverse",
"total_length": 46,
"trace_id": "9b213fb2-0821-4586-8b73-7ac2859d31e4"
},
"seed": 7387085,
"task_id": 407387085,
"task_type": "dyck_language2"
} |
logic-v2 | Q: What opening brackets should precede "<>⟨⟩⟨⟩()⟨⟩[]⟨⟩⟩)()>[])>[]}" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{<(<(⟨<>⟨⟩⟨⟩()⟨⟩[]⟨⟩⟩)()>[])>[]}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "{<(<(⟨<>⟨⟩⟨⟩()⟨⟩[]⟨⟩⟩)()>[])>[]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{<(<(⟨",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 45246791,
"suffix_sequence": "<>⟨⟩⟨⟩()⟨⟩[]⟨⟩⟩)()>[])>[]}",
"task_type": "reverse",
"total_length": 32,
"trace_id": "6c8371e1-2f9f-4b66-9c12-f29b335f1255"
},
"question": "Q: What opening brackets should precede \"<>⟨⟩⟨⟩()⟨⟩[]⟨⟩⟩)()>[])>[]}\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 6,
"full_sequence": "{<(<(⟨<>⟨⟩⟨⟩()⟨⟩[]⟨⟩⟩)()>[])>[]}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{<(<(⟨",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 45246791,
"suffix_sequence": "<>⟨⟩⟨⟩()⟨⟩[]⟨⟩⟩)()>[])>[]}",
"task_type": "reverse",
"total_length": 32,
"trace_id": "6c8371e1-2f9f-4b66-9c12-f29b335f1255"
},
"seed": 45246791,
"task_id": 445246791,
"task_type": "dyck_language2"
} |
logic-v2 | Fill in the blank:
_____ + }⟩⦃⦄<>())()>()⟩>⦃⦄⦄⟩)⦄[]⟩⦄⦃⦄()⟨⟩()⟦⟧⟦⟧⟨⟩[]⦃⦄⟦⟧ = valid Dyck sequence
Rules:
- The blank contains only opening brackets
- Use the minimum required
Please provide your final answer (the complete filled sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⟨⦃(⟨⦃<⟨<(⟨{}⟩⦃⦄<>())()>()⟩>⦃⦄⦄⟩)⦄[]⟩⦄⦃⦄()⟨⟩()⟦⟧⟦⟧⟨⟩[]⦃⦄⟦⟧",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "⦃⟨⦃(⟨⦃<⟨<(⟨{}⟩⦃⦄<>())()>()⟩>⦃⦄⦄⟩)⦄[]⟩⦄⦃⦄()⟨⟩()⟦⟧⟦⟧⟨⟩[]⦃⦄⟦⟧",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⟨⦃(⟨⦃<⟨<(⟨{",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 66546567,
"suffix_sequence": "}⟩⦃⦄<>())()>()⟩>⦃⦄⦄⟩)⦄[]⟩⦄⦃⦄()⟨⟩()⟦⟧⟦⟧⟨⟩[]⦃⦄⟦⟧",
"task_type": "reverse",
"total_length": 58,
"trace_id": "01c948ab-cda9-4129-b690-2ba356432c1a"
},
"question": "Fill in the blank:\n\n_____ + }⟩⦃⦄<>())()>()⟩>⦃⦄⦄⟩)⦄[]⟩⦄⦃⦄()⟨⟩()⟦⟧⟦⟧⟨⟩[]⦃⦄⟦⟧ = valid Dyck sequence\n\nRules:\n- The blank contains only opening brackets\n- Use the minimum required\n\nPlease provide your final answer (the complete filled sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 12,
"full_sequence": "⦃⟨⦃(⟨⦃<⟨<(⟨{}⟩⦃⦄<>())()>()⟩>⦃⦄⦄⟩)⦄[]⟩⦄⦃⦄()⟨⟩()⟦⟧⟦⟧⟨⟩[]⦃⦄⟦⟧",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⟨⦃(⟨⦃<⟨<(⟨{",
"prompt_name": "fill_in",
"prompt_variant": 7,
"seed": 66546567,
"suffix_sequence": "}⟩⦃⦄<>())()>()⟩>⦃⦄⦄⟩)⦄[]⟩⦄⦃⦄()⟨⟩()⟦⟧⟦⟧⟨⟩[]⦃⦄⟦⟧",
"task_type": "reverse",
"total_length": 58,
"trace_id": "01c948ab-cda9-4129-b690-2ba356432c1a"
},
"seed": 66546567,
"task_id": 466546567,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"[]})⦃⦄)}⟧⟦⟧⟨⟩⟦⟧})}}⟨⟩<>⦄{})()⦃⦄⦄⟩()[]<>()"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨⦃(⦃{{({⟦{(({[]})⦃⦄)}⟧⟦⟧⟨⟩⟦⟧})}}⟨⟩<>⦄{})()⦃⦄⦄⟩()[]<>()",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "⟨⦃(⦃{{({⟦{(({[]})⦃⦄)}⟧⟦⟧⟨⟩⟦⟧})}}⟨⟩<>⦄{})()⦃⦄⦄⟩()[]<>()",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⦃(⦃{{({⟦{(({",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 45451568,
"suffix_sequence": "[]})⦃⦄)}⟧⟦⟧⟨⟩⟦⟧})}}⟨⟩<>⦄{})()⦃⦄⦄⟩()[]<>()",
"task_type": "reverse",
"total_length": 54,
"trace_id": "22c1d99c-d644-445d-94c3-204d7b8d75c4"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\"[]})⦃⦄)}⟧⟦⟧⟨⟩⟦⟧})}}⟨⟩<>⦄{})()⦃⦄⦄⟩()[]<>()\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 13,
"full_sequence": "⟨⦃(⦃{{({⟦{(({[]})⦃⦄)}⟧⟦⟧⟨⟩⟦⟧})}}⟨⟩<>⦄{})()⦃⦄⦄⟩()[]<>()",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⦃(⦃{{({⟦{(({",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 45451568,
"suffix_sequence": "[]})⦃⦄)}⟧⟦⟧⟨⟩⟦⟧})}}⟨⟩<>⦄{})()⦃⦄⦄⟩()[]<>()",
"task_type": "reverse",
"total_length": 54,
"trace_id": "22c1d99c-d644-445d-94c3-204d7b8d75c4"
},
"seed": 45451568,
"task_id": 445451568,
"task_type": "dyck_language2"
} |
logic-v2 | Q: What opening brackets should precede "{}}<>){}⟧⟩>⦄<>]⟦⟧>)()⦄⦃⦄{}()[]⟩⟨⟩[][]⦄⦃⦄⟦⟧⦃⦄⦃⦄" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⦃⟨⦃(<[⦃<⟨⟦({{}}<>){}⟧⟩>⦄<>]⟦⟧>)()⦄⦃⦄{}()[]⟩⟨⟩[][]⦄⦃⦄⟦⟧⦃⦄⦃⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "⦃⟨⦃(<[⦃<⟨⟦({{}}<>){}⟧⟩>⦄<>]⟦⟧>)()⦄⦃⦄{}()[]⟩⟨⟩[][]⦄⦃⦄⟦⟧⦃⦄⦃⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⟨⦃(<[⦃<⟨⟦({",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 66750888,
"suffix_sequence": "{}}<>){}⟧⟩>⦄<>]⟦⟧>)()⦄⦃⦄{}()[]⟩⟨⟩[][]⦄⦃⦄⟦⟧⦃⦄⦃⦄",
"task_type": "reverse",
"total_length": 58,
"trace_id": "4eb69073-f8fa-41ba-be0b-e80f0b92d5b6"
},
"question": "Q: What opening brackets should precede \"{}}<>){}⟧⟩>⦄<>]⟦⟧>)()⦄⦃⦄{}()[]⟩⟨⟩[][]⦄⦃⦄⟦⟧⦃⦄⦃⦄\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 12,
"full_sequence": "⦃⟨⦃(<[⦃<⟨⟦({{}}<>){}⟧⟩>⦄<>]⟦⟧>)()⦄⦃⦄{}()[]⟩⟨⟩[][]⦄⦃⦄⟦⟧⦃⦄⦃⦄",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⦃⟨⦃(<[⦃<⟨⟦({",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 66750888,
"suffix_sequence": "{}}<>){}⟧⟩>⦄<>]⟦⟧>)()⦄⦃⦄{}()[]⟩⟨⟩[][]⦄⦃⦄⟦⟧⦃⦄⦃⦄",
"task_type": "reverse",
"total_length": 58,
"trace_id": "4eb69073-f8fa-41ba-be0b-e80f0b92d5b6"
},
"seed": 66750888,
"task_id": 466750888,
"task_type": "dyck_language2"
} |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ]]⟩⟩]}}[]{}<>{}
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "{{[⟨⟨[[]]⟩⟩]}}[]{}<>{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 7,
"full_sequence": "{{[⟨⟨[[]]⟩⟩]}}[]{}<>{}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{{[⟨⟨[[",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 81378256,
"suffix_sequence": "]]⟩⟩]}}[]{}<>{}",
"task_type": "reverse",
"total_length": 22,
"trace_id": "0b41daed-258b-4fcd-b47f-037af2e01da5"
},
"question": "[DYCK LANGUAGE TASK]\n\nINPUT: ]]⟩⟩]}}[]{}<>{}\nDIRECTION: reverse (prepend opening brackets)\n\nCONSTRAINTS:\n- Minimize added brackets\n- Result must be valid Dyck word\n- Preserve input as suffix\n\nPlease provide your final answer in backticks like `answer`."
},
"metadata": {
"fill_length": 7,
"full_sequence": "{{[⟨⟨[[]]⟩⟩]}}[]{}<>{}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{{[⟨⟨[[",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 81378256,
"suffix_sequence": "]]⟩⟩]}}[]{}<>{}",
"task_type": "reverse",
"total_length": 22,
"trace_id": "0b41daed-258b-4fcd-b47f-037af2e01da5"
},
"seed": 81378256,
"task_id": 481378256,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"}⟧⟧⟩})⟧⟧))]⟧>>}⟧>>"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<<⟦{<<⟦[((⟦⟦({⟨⟦⟦{}⟧⟧⟩})⟧⟧))]⟧>>}⟧>>",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"full_sequence": "<<⟦{<<⟦[((⟦⟦({⟨⟦⟦{}⟧⟧⟩})⟧⟧))]⟧>>}⟧>>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<⟦{<<⟦[((⟦⟦({⟨⟦⟦{",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 54901116,
"suffix_sequence": "}⟧⟧⟩})⟧⟧))]⟧>>}⟧>>",
"task_type": "reverse",
"total_length": 36,
"trace_id": "4aab70cf-ece4-4d11-9ff4-6e0d8f66d652"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\"}⟧⟧⟩})⟧⟧))]⟧>>}⟧>>\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 18,
"full_sequence": "<<⟦{<<⟦[((⟦⟦({⟨⟦⟦{}⟧⟧⟩})⟧⟧))]⟧>>}⟧>>",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<<⟦{<<⟦[((⟦⟦({⟨⟦⟦{",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 54901116,
"suffix_sequence": "}⟧⟧⟩})⟧⟧))]⟧>>}⟧>>",
"task_type": "reverse",
"total_length": 36,
"trace_id": "4aab70cf-ece4-4d11-9ff4-6e0d8f66d652"
},
"seed": 54901116,
"task_id": 454901116,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"⦄>⦄)⟩"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "⟨(⦃<⦃⦄>⦄)⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "⟨(⦃<⦃⦄>⦄)⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨(⦃<⦃",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 77670110,
"suffix_sequence": "⦄>⦄)⟩",
"task_type": "reverse",
"total_length": 10,
"trace_id": "1bfa9fe0-375e-445f-977d-d4aba9535e89"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\"⦄>⦄)⟩\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 5,
"full_sequence": "⟨(⦃<⦃⦄>⦄)⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨(⦃<⦃",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 77670110,
"suffix_sequence": "⦄>⦄)⟩",
"task_type": "reverse",
"total_length": 10,
"trace_id": "1bfa9fe0-375e-445f-977d-d4aba9535e89"
},
"seed": 77670110,
"task_id": 477670110,
"task_type": "dyck_language2"
} |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ><>}{}><>}⟨⟩{}⟩])⟨⟩{})}{}]]>⟩}
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "{⟨<[[{(([⟨{<{<><>}{}><>}⟨⟩{}⟩])⟨⟩{})}{}]]>⟩}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 14,
"full_sequence": "{⟨<[[{(([⟨{<{<><>}{}><>}⟨⟩{}⟩])⟨⟩{})}{}]]>⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨<[[{(([⟨{<{<",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 19074529,
"suffix_sequence": "><>}{}><>}⟨⟩{}⟩])⟨⟩{})}{}]]>⟩}",
"task_type": "reverse",
"total_length": 44,
"trace_id": "947a2e41-8af6-4faf-904c-acafa6be98db"
},
"question": "[DYCK LANGUAGE TASK]\n\nINPUT: ><>}{}><>}⟨⟩{}⟩])⟨⟩{})}{}]]>⟩}\nDIRECTION: reverse (prepend opening brackets)\n\nCONSTRAINTS:\n- Minimize added brackets\n- Result must be valid Dyck word\n- Preserve input as suffix\n\nPlease provide your final answer in backticks like `answer`."
},
"metadata": {
"fill_length": 14,
"full_sequence": "{⟨<[[{(([⟨{<{<><>}{}><>}⟨⟩{}⟩])⟨⟩{})}{}]]>⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨<[[{(([⟨{<{<",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 19074529,
"suffix_sequence": "><>}{}><>}⟨⟩{}⟩])⟨⟩{})}{}]]>⟩}",
"task_type": "reverse",
"total_length": 44,
"trace_id": "947a2e41-8af6-4faf-904c-acafa6be98db"
},
"seed": 19074529,
"task_id": 419074529,
"task_type": "dyck_language2"
} |
logic-v2 | Bracket Puzzle: What's missing at the start?
Given suffix: ){}){}[])
Solve:
1. Each closing bracket needs a matching opening bracket
2. Add the minimal opening brackets to the left
3. The final sequence must be properly nested
Please provide your final answer (the full balanced sequence) in backticks like `answer`. | {
"game_data": {
"answer": "(((){}){}[])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "(((){}){}[])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(((",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 39252039,
"suffix_sequence": "){}){}[])",
"task_type": "reverse",
"total_length": 12,
"trace_id": "0c9283bd-561d-4476-b4ba-1ba2ee59645e"
},
"question": "Bracket Puzzle: What's missing at the start?\n\nGiven suffix: ){}){}[])\n\nSolve:\n1. Each closing bracket needs a matching opening bracket\n2. Add the minimal opening brackets to the left\n3. The final sequence must be properly nested\n\nPlease provide your final answer (the full balanced sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 3,
"full_sequence": "(((){}){}[])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "(((",
"prompt_name": "puzzle",
"prompt_variant": 2,
"seed": 39252039,
"suffix_sequence": "){}){}[])",
"task_type": "reverse",
"total_length": 12,
"trace_id": "0c9283bd-561d-4476-b4ba-1ba2ee59645e"
},
"seed": 39252039,
"task_id": 439252039,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = ">{}[]⟧>{}}⦃⦄" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "{<⟦<>{}[]⟧>{}}⦃⦄",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 4,
"full_sequence": "{<⟦<>{}[]⟧>{}}⦃⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "{<⟦<",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 15432943,
"suffix_sequence": ">{}[]⟧>{}}⦃⦄",
"task_type": "reverse",
"total_length": 16,
"trace_id": "838292bf-664b-4074-bd33-d5e71c1209e3"
},
"question": "Let S = \">{}[]⟧>{}}⦃⦄\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 4,
"full_sequence": "{<⟦<>{}[]⟧>{}}⦃⦄",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "{<⟦<",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 15432943,
"suffix_sequence": ">{}[]⟧>{}}⦃⦄",
"task_type": "reverse",
"total_length": 16,
"trace_id": "838292bf-664b-4074-bd33-d5e71c1209e3"
},
"seed": 15432943,
"task_id": 415432943,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "[])]}]}]}])]}]}]}])" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "([{[{[{[([{[{[{[([])]}]}]}])]}]}]}])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 17,
"full_sequence": "([{[{[{[([{[{[{[([])]}]}]}])]}]}]}])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{[{[{[([{[{[{[(",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 77348192,
"suffix_sequence": "[])]}]}]}])]}]}]}])",
"task_type": "reverse",
"total_length": 36,
"trace_id": "0e625085-c800-4d8f-9a55-8f10c32e5f73"
},
"question": "Let S = \"[])]}]}]}])]}]}]}])\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 17,
"full_sequence": "([{[{[{[([{[{[{[([])]}]}]}])]}]}]}])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{[{[{[([{[{[{[(",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 77348192,
"suffix_sequence": "[])]}]}]}])]}]}]}])",
"task_type": "reverse",
"total_length": 36,
"trace_id": "0e625085-c800-4d8f-9a55-8f10c32e5f73"
},
"seed": 77348192,
"task_id": 477348192,
"task_type": "dyck_language2"
} |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: }{}}}]])]}])
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pairs beyond what is required
Please provide your final answer (the complete valid sequence) in backticks like `answer`. | {
"game_data": {
"answer": "([{[([[{{{}{}}}]])]}])",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 10,
"full_sequence": "([{[([[{{{}{}}}]])]}])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{[([[{{{",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 11091898,
"suffix_sequence": "}{}}}]])]}])",
"task_type": "reverse",
"total_length": 22,
"trace_id": "0e10845e-6535-4cbf-8362-4866ef54fe70"
},
"question": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: }{}}}]])]}])\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do not add any extra bracket pairs beyond what is required\n\nPlease provide your final answer (the complete valid sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 10,
"full_sequence": "([{[([[{{{}{}}}]])]}])",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "([{[([[{{{",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 11091898,
"suffix_sequence": "}{}}}]])]}])",
"task_type": "reverse",
"total_length": 22,
"trace_id": "0e10845e-6535-4cbf-8362-4866ef54fe70"
},
"seed": 11091898,
"task_id": 411091898,
"task_type": "dyck_language2"
} |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ⦆⦄⟧⦆)}{}
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pairs beyond what is required
Please provide your final answer (the complete valid sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{(⦅⟦⦃⦅⦆⦄⟧⦆)}{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "{(⦅⟦⦃⦅⦆⦄⟧⦆)}{}",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "{(⦅⟦⦃⦅",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 16198689,
"suffix_sequence": "⦆⦄⟧⦆)}{}",
"task_type": "reverse",
"total_length": 14,
"trace_id": "e3e1f5f4-9301-46c2-bb84-f3cfb316ee8d"
},
"question": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ⦆⦄⟧⦆)}{}\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do not add any extra bracket pairs beyond what is required\n\nPlease provide your final answer (the complete valid sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 6,
"full_sequence": "{(⦅⟦⦃⦅⦆⦄⟧⦆)}{}",
"n_types": 8,
"nesting_depth": 0,
"opening_prefix": "{(⦅⟦⦃⦅",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 16198689,
"suffix_sequence": "⦆⦄⟧⦆)}{}",
"task_type": "reverse",
"total_length": 14,
"trace_id": "e3e1f5f4-9301-46c2-bb84-f3cfb316ee8d"
},
"seed": 16198689,
"task_id": 416198689,
"task_type": "dyck_language2"
} |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: ()})]
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pairs beyond what is required
Please provide your final answer (the complete valid sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[({()})]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 3,
"full_sequence": "[({()})]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[({",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 29831745,
"suffix_sequence": "()})]",
"task_type": "reverse",
"total_length": 8,
"trace_id": "473df2fa-7598-43cd-ac78-86f705617e3c"
},
"question": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: ()})]\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do not add any extra bracket pairs beyond what is required\n\nPlease provide your final answer (the complete valid sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 3,
"full_sequence": "[({()})]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[({",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 29831745,
"suffix_sequence": "()})]",
"task_type": "reverse",
"total_length": 8,
"trace_id": "473df2fa-7598-43cd-ac78-86f705617e3c"
},
"seed": 29831745,
"task_id": 429831745,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"}}}}[])()))}[]])[]][])()})()()[][]{}(){}"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "({([([{((({{{{}}}}[])()))}[]])[]][])()})()()[][]{}(){}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 14,
"full_sequence": "({([([{((({{{{}}}}[])()))}[]])[]][])()})()()[][]{}(){}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({([([{((({{{{",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 70207559,
"suffix_sequence": "}}}}[])()))}[]])[]][])()})()()[][]{}(){}",
"task_type": "reverse",
"total_length": 54,
"trace_id": "3d9a3295-5a71-4915-b33f-c80d6b7b247c"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\"}}}}[])()))}[]])[]][])()})()()[][]{}(){}\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 14,
"full_sequence": "({([([{((({{{{}}}}[])()))}[]])[]][])()})()()[][]{}(){}",
"n_types": 3,
"nesting_depth": 0,
"opening_prefix": "({([([{((({{{{",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 70207559,
"suffix_sequence": "}}}}[])()))}[]])[]][])()})()()[][]{}(){}",
"task_type": "reverse",
"total_length": 54,
"trace_id": "3d9a3295-5a71-4915-b33f-c80d6b7b247c"
},
"seed": 70207559,
"task_id": 470207559,
"task_type": "dyck_language2"
} |
logic-v2 | Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.
Suffix: }>)<>)⟩)⟩}⟩]⟩)}⟩⟩)⟩}
Rules:
- Add only the opening brackets needed to match all unmatched closing brackets
- The opening brackets should be prepended to form a valid sequence
- Do not add any extra bracket pairs beyond what is required
Please provide your final answer (the complete valid sequence) in backticks like `answer`. | {
"game_data": {
"answer": "{⟨(⟨⟨{(⟨[⟨{⟨(⟨((<{}>)<>)⟩)⟩}⟩]⟩)}⟩⟩)⟩}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 18,
"full_sequence": "{⟨(⟨⟨{(⟨[⟨{⟨(⟨((<{}>)<>)⟩)⟩}⟩]⟩)}⟩⟩)⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨(⟨⟨{(⟨[⟨{⟨(⟨((<{",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 6780798,
"suffix_sequence": "}>)<>)⟩)⟩}⟩]⟩)}⟩⟩)⟩}",
"task_type": "reverse",
"total_length": 38,
"trace_id": "40134b54-0376-4edd-865e-30318e6b146d"
},
"question": "Complete the following Dyck language sequence by adding the minimal necessary opening brackets at the beginning.\n\nSuffix: }>)<>)⟩)⟩}⟩]⟩)}⟩⟩)⟩}\n\nRules:\n- Add only the opening brackets needed to match all unmatched closing brackets\n- The opening brackets should be prepended to form a valid sequence\n- Do not add any extra bracket pairs beyond what is required\n\nPlease provide your final answer (the complete valid sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 18,
"full_sequence": "{⟨(⟨⟨{(⟨[⟨{⟨(⟨((<{}>)<>)⟩)⟩}⟩]⟩)}⟩⟩)⟩}",
"n_types": 5,
"nesting_depth": 0,
"opening_prefix": "{⟨(⟨⟨{(⟨[⟨{⟨(⟨((<{",
"prompt_name": "direct",
"prompt_variant": 0,
"seed": 6780798,
"suffix_sequence": "}>)<>)⟩)⟩}⟩]⟩)}⟩⟩)⟩}",
"task_type": "reverse",
"total_length": 38,
"trace_id": "40134b54-0376-4edd-865e-30318e6b146d"
},
"seed": 6780798,
"task_id": 406780798,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"])⟩])<>⟩⟧<>{}<>]{})}}⟨⟩>⟩>{}"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "<⟨<{{([⟦⟨([⟨([])⟩])<>⟩⟧<>{}<>]{})}}⟨⟩>⟩>{}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 14,
"full_sequence": "<⟨<{{([⟦⟨([⟨([])⟩])<>⟩⟧<>{}<>]{})}}⟨⟩>⟩>{}",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟨<{{([⟦⟨([⟨([",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 53509421,
"suffix_sequence": "])⟩])<>⟩⟧<>{}<>]{})}}⟨⟩>⟩>{}",
"task_type": "reverse",
"total_length": 42,
"trace_id": "5d7faec5-d5eb-4de4-8189-e4cb08c6e757"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\"])⟩])<>⟩⟧<>{}<>]{})}}⟨⟩>⟩>{}\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 14,
"full_sequence": "<⟨<{{([⟦⟨([⟨([])⟩])<>⟩⟧<>{}<>]{})}}⟨⟩>⟩>{}",
"n_types": 6,
"nesting_depth": 0,
"opening_prefix": "<⟨<{{([⟦⟨([⟨([",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 53509421,
"suffix_sequence": "])⟩])<>⟩⟧<>{}<>]{})}}⟨⟩>⟩>{}",
"task_type": "reverse",
"total_length": 42,
"trace_id": "5d7faec5-d5eb-4de4-8189-e4cb08c6e757"
},
"seed": 53509421,
"task_id": 453509421,
"task_type": "dyck_language2"
} |
logic-v2 | Q: What opening brackets should precede "()]]))][]>[]()<>}}]" to form a valid bracket sequence?
Requirements:
- Use exactly the brackets needed (no more, no less)
- Maintain proper nesting order
Please provide your final answer (the entire resulting sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[{{<[(([[()]]))][]>[]()<>}}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 9,
"full_sequence": "[{{<[(([[()]]))][]>[]()<>}}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{{<[(([[",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 48339695,
"suffix_sequence": "()]]))][]>[]()<>}}]",
"task_type": "reverse",
"total_length": 28,
"trace_id": "486fe320-5216-4210-9e54-3ae5528dd4ec"
},
"question": "Q: What opening brackets should precede \"()]]))][]>[]()<>}}]\" to form a valid bracket sequence?\n\nRequirements:\n- Use exactly the brackets needed (no more, no less)\n- Maintain proper nesting order\n\nPlease provide your final answer (the entire resulting sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 9,
"full_sequence": "[{{<[(([[()]]))][]>[]()<>}}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{{<[(([[",
"prompt_name": "qa",
"prompt_variant": 6,
"seed": 48339695,
"suffix_sequence": "()]]))][]>[]()<>}}]",
"task_type": "reverse",
"total_length": 28,
"trace_id": "486fe320-5216-4210-9e54-3ae5528dd4ec"
},
"seed": 48339695,
"task_id": 448339695,
"task_type": "dyck_language2"
} |
logic-v2 | A sequence of brackets was cut, and only the end remains:
"<>}]{}})()<>{}>]<><>(){}"
Restore the missing beginning so that:
- Every closing bracket has its opening partner
- No extra brackets are added
- The sequence is properly nested
Please provide your final answer (the restored complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[<({[{<>}]{}})()<>{}>]<><>(){}",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "[<({[{<>}]{}})()<>{}>]<><>(){}",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<({[{",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 82847419,
"suffix_sequence": "<>}]{}})()<>{}>]<><>(){}",
"task_type": "reverse",
"total_length": 30,
"trace_id": "60d60c51-6b4a-45ce-a98b-25883b0a4c42"
},
"question": "A sequence of brackets was cut, and only the end remains:\n\n\"<>}]{}})()<>{}>]<><>(){}\"\n\nRestore the missing beginning so that:\n- Every closing bracket has its opening partner\n- No extra brackets are added\n- The sequence is properly nested\n\nPlease provide your final answer (the restored complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 6,
"full_sequence": "[<({[{<>}]{}})()<>{}>]<><>(){}",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<({[{",
"prompt_name": "story",
"prompt_variant": 4,
"seed": 82847419,
"suffix_sequence": "<>}]{}})()<>{}>]<><>(){}",
"task_type": "reverse",
"total_length": 30,
"trace_id": "60d60c51-6b4a-45ce-a98b-25883b0a4c42"
},
"seed": 82847419,
"task_id": 482847419,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "())()[]{}{}{})}]}]" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "[{[{((())()[]{}{}{})}]}]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 6,
"full_sequence": "[{[{((())()[]{}{}{})}]}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{[{((",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 4857039,
"suffix_sequence": "())()[]{}{}{})}]}]",
"task_type": "reverse",
"total_length": 24,
"trace_id": "fa30a9aa-6d7b-474f-a924-b4ba51a2b128"
},
"question": "Let S = \"())()[]{}{}{})}]}]\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 6,
"full_sequence": "[{[{((())()[]{}{}{})}]}]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[{[{((",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 4857039,
"suffix_sequence": "())()[]{}{}{})}]}]",
"task_type": "reverse",
"total_length": 24,
"trace_id": "fa30a9aa-6d7b-474f-a924-b4ba51a2b128"
},
"seed": 4857039,
"task_id": 404857039,
"task_type": "dyck_language2"
} |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: )]{}>)]
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "[(<[()]{}>)]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 5,
"full_sequence": "[(<[()]{}>)]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[(<[(",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 30117195,
"suffix_sequence": ")]{}>)]",
"task_type": "reverse",
"total_length": 12,
"trace_id": "e8638b9a-c29b-42f0-aba6-c6f5d29e93ad"
},
"question": "[DYCK LANGUAGE TASK]\n\nINPUT: )]{}>)]\nDIRECTION: reverse (prepend opening brackets)\n\nCONSTRAINTS:\n- Minimize added brackets\n- Result must be valid Dyck word\n- Preserve input as suffix\n\nPlease provide your final answer in backticks like `answer`."
},
"metadata": {
"fill_length": 5,
"full_sequence": "[(<[()]{}>)]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[(<[(",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 30117195,
"suffix_sequence": ")]{}>)]",
"task_type": "reverse",
"total_length": 12,
"trace_id": "e8638b9a-c29b-42f0-aba6-c6f5d29e93ad"
},
"seed": 30117195,
"task_id": 430117195,
"task_type": "dyck_language2"
} |
logic-v2 | [DYCK LANGUAGE TASK]
INPUT: ⟧⦃⦄]⟨⟩()[]()()⟦⟧{}⦃⦄⟧<>⟩⟦⟧}⟦⟧>{}⟦⟧⦃⦄⟦⟧])⦃⦄⦃⦄⦄⦄⦄⟩
DIRECTION: reverse (prepend opening brackets)
CONSTRAINTS:
- Minimize added brackets
- Result must be valid Dyck word
- Preserve input as suffix
Please provide your final answer in backticks like `answer`. | {
"game_data": {
"answer": "⟨⦃⦃⦃([<{⟨⟦[⟦⟧⦃⦄]⟨⟩()[]()()⟦⟧{}⦃⦄⟧<>⟩⟦⟧}⟦⟧>{}⟦⟧⦃⦄⟦⟧])⦃⦄⦃⦄⦄⦄⦄⟩",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 12,
"full_sequence": "⟨⦃⦃⦃([<{⟨⟦[⟦⟧⦃⦄]⟨⟩()[]()()⟦⟧{}⦃⦄⟧<>⟩⟦⟧}⟦⟧>{}⟦⟧⦃⦄⟦⟧])⦃⦄⦃⦄⦄⦄⦄⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⦃⦃⦃([<{⟨⟦[⟦",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 83149870,
"suffix_sequence": "⟧⦃⦄]⟨⟩()[]()()⟦⟧{}⦃⦄⟧<>⟩⟦⟧}⟦⟧>{}⟦⟧⦃⦄⟦⟧])⦃⦄⦃⦄⦄⦄⦄⟩",
"task_type": "reverse",
"total_length": 60,
"trace_id": "65bac42f-26d2-4773-9805-2f3aae1be8e4"
},
"question": "[DYCK LANGUAGE TASK]\n\nINPUT: ⟧⦃⦄]⟨⟩()[]()()⟦⟧{}⦃⦄⟧<>⟩⟦⟧}⟦⟧>{}⟦⟧⦃⦄⟦⟧])⦃⦄⦃⦄⦄⦄⦄⟩\nDIRECTION: reverse (prepend opening brackets)\n\nCONSTRAINTS:\n- Minimize added brackets\n- Result must be valid Dyck word\n- Preserve input as suffix\n\nPlease provide your final answer in backticks like `answer`."
},
"metadata": {
"fill_length": 12,
"full_sequence": "⟨⦃⦃⦃([<{⟨⟦[⟦⟧⦃⦄]⟨⟩()[]()()⟦⟧{}⦃⦄⟧<>⟩⟦⟧}⟦⟧>{}⟦⟧⦃⦄⟦⟧])⦃⦄⦃⦄⦄⦄⦄⟩",
"n_types": 7,
"nesting_depth": 0,
"opening_prefix": "⟨⦃⦃⦃([<{⟨⟦[⟦",
"prompt_name": "technical",
"prompt_variant": 3,
"seed": 83149870,
"suffix_sequence": "⟧⦃⦄]⟨⟩()[]()()⟦⟧{}⦃⦄⟧<>⟩⟦⟧}⟦⟧>{}⟦⟧⦃⦄⟦⟧])⦃⦄⦃⦄⦄⦄⦄⟩",
"task_type": "reverse",
"total_length": 60,
"trace_id": "65bac42f-26d2-4773-9805-2f3aae1be8e4"
},
"seed": 83149870,
"task_id": 483149870,
"task_type": "dyck_language2"
} |
logic-v2 | You are given the ending portion of a bracket sequence. Find the beginning.
Ending: []>>})()}{}})>)]>)>))]
Your task:
- Determine what opening brackets must come before this ending
- The result must be a valid, balanced bracket sequence
- Use the minimum number of opening brackets necessary
Please provide your final answer (the complete sequence) in backticks like `answer`. | {
"game_data": {
"answer": "[((<(<[(<({{({<<[]>>})()}{}})>)]>)>))]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 16,
"full_sequence": "[((<(<[(<({{({<<[]>>})()}{}})>)]>)>))]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[((<(<[(<({{({<<",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 47187858,
"suffix_sequence": "[]>>})()}{}})>)]>)>))]",
"task_type": "reverse",
"total_length": 38,
"trace_id": "e517cf2e-0ff5-47de-a29e-7de976d74b46"
},
"question": "You are given the ending portion of a bracket sequence. Find the beginning.\n\nEnding: []>>})()}{}})>)]>)>))]\n\nYour task:\n- Determine what opening brackets must come before this ending\n- The result must be a valid, balanced bracket sequence\n- Use the minimum number of opening brackets necessary\n\nPlease provide your final answer (the complete sequence) in backticks like `answer`."
},
"metadata": {
"fill_length": 16,
"full_sequence": "[((<(<[(<({{({<<[]>>})()}{}})>)]>)>))]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[((<(<[(<({{({<<",
"prompt_name": "reverse_perspective",
"prompt_variant": 1,
"seed": 47187858,
"suffix_sequence": "[]>>})()}{}})>)]>)>))]",
"task_type": "reverse",
"total_length": 38,
"trace_id": "e517cf2e-0ff5-47de-a29e-7de976d74b46"
},
"seed": 47187858,
"task_id": 447187858,
"task_type": "dyck_language2"
} |
logic-v2 | Let S = "])][]<>>}][]>}]}>>]" be a suffix of a Dyck word.
Find the minimal prefix P such that P + S forms a valid Dyck word.
Please provide your final answer (P + S, the complete Dyck word) in backticks like `answer`. | {
"game_data": {
"answer": "[<<{[{<[{<[([])][]<>>}][]>}]}>>]",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"fill_length": 13,
"full_sequence": "[<<{[{<[{<[([])][]<>>}][]>}]}>>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<<{[{<[{<[([",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 77842272,
"suffix_sequence": "])][]<>>}][]>}]}>>]",
"task_type": "reverse",
"total_length": 32,
"trace_id": "e69324cf-3281-4ba6-87d2-cb3a113a8068"
},
"question": "Let S = \"])][]<>>}][]>}]}>>]\" be a suffix of a Dyck word.\n\nFind the minimal prefix P such that P + S forms a valid Dyck word.\n\nPlease provide your final answer (P + S, the complete Dyck word) in backticks like `answer`."
},
"metadata": {
"fill_length": 13,
"full_sequence": "[<<{[{<[{<[([])][]<>>}][]>}]}>>]",
"n_types": 4,
"nesting_depth": 0,
"opening_prefix": "[<<{[{<[{<[([",
"prompt_name": "mathematical",
"prompt_variant": 5,
"seed": 77842272,
"suffix_sequence": "])][]<>>}][]>}]}>>]",
"task_type": "reverse",
"total_length": 32,
"trace_id": "e69324cf-3281-4ba6-87d2-cb3a113a8068"
},
"seed": 77842272,
"task_id": 477842272,
"task_type": "dyck_language2"
} |
End of preview. Expand
in Data Studio
README.md exists but content is empty.
- Downloads last month
- 4