RecurrReason: Recurrent Reasoning on Symbolic Puzzles

A difficulty-controlled benchmark for evaluating multi-step reasoning in language models

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📋 Table of Contents

• Overview
• Dataset Structure
• Puzzles
• Quick Start
• Citation
• License

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🎯 Overview

RecurrReason is a benchmark of four recurrent logic puzzles with optimal trajectories and controlled difficulty scaling (N=1 to 10). It tests whether language models can:

• Find optimal (minimal-length) solutions
• Produce valid intermediate steps
• Generalize to harder out-of-distribution instances

Metric	Value
Total Puzzles	10,817
Total Moves	285,933
Puzzle Types	4
Difficulty Range	N=1 to 10

Current reasoning benchmarks often test only final answer correctness. RecurrReason evaluates:

• Move validity: Are all intermediate steps legal?
• Optimality: Is the solution minimal-length?
• Length generalization: Does performance hold on longer sequences?

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📊 Dataset Structure

Data Splits

Split	N Range	Purpose
Train	N=1-7	In-distribution training data
Test (OOD)	N=8-10	Out-of-distribution evaluation

Note: We provide train and test splits. Users can create their own validation split from the training data if needed.

File Structure

RecurrReason/
├── Block World/
│   ├── bw_train_1_7.csv
│   └── bw_test_8_10.csv
├── Checkers Jumping/
│   ├── cj_train_1_7.csv
│   └── cj_test_8_10.csv
├── Tower of Hanoi/
│   ├── toh_train_1_7.csv
│   └── toh_test_8_10.csv
├── River Crossing/
│   ├── rc_train_1_7.csv
│   └── rc_test_8_10.csv
└── README.md (this file)

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🧩 Puzzles

RecurrReason contains four diverse logic puzzles with different structural properties:

Puzzle	Difficulty	Solution Length	Transition Locality	Puzzles	Moves
Block World	⭐⭐	O(N)	O(1)	849	5,827
Checkers Jumping	⭐⭐⭐	(N+1)²−1	O(N)	5,700	242,494
Tower of Hanoi	⭐⭐⭐⭐⭐	2^N−1	O(N)	60	12,216
River Crossing	⭐⭐⭐⭐	Variable	O(N) global	4,208	25,396

Click on each puzzle name for detailed documentation including:

• Puzzle rules and constraints
• State representation format
• Example trajectories
• Column descriptions

Quick Puzzle Descriptions

Block World - Rearrange blocks in stacks

Goal: Move blocks from initial configuration to target configuration.

Rules:

• Only top block of a stack can be moved
• Can place on empty stack or on top of another block

Why interesting: O(1) transition locality makes it learnable and tests dependency reasoning.

→ Full documentation

Checkers Jumping - Swap red and blue checkers

Goal: Swap N red and N blue checkers on a 1D board with one empty space between them.

Rules:

• Red moves only right, blue only left (and vice versa based on starting configuration)
• Can slide to adjacent empty space or jump over opposite color

Why interesting: Quadratic solution length and tests avoiding dead-end configurations.

→ Full documentation

Tower of Hanoi - Transfer disks between pegs

Goal: Move N disks from source peg to target peg across 3 pegs.

Rules:

• Move one disk at a time
• Only topmost disk can be moved
• Larger disk cannot be on top of a smaller disk

Why interesting: Exponential solution length (2^N−1). It is a classic recursive problem.

→ Full documentation

River Crossing - Transport agents safely

Goal: Transport N actor-agent pairs across river using boat with capacity k.

Rules:

• Boat holds at most k individuals
• Actor aᵢ cannot be with agent Aⱼ (j≠i) unless agent Aᵢ is present

Why interesting: Global O(N) constraint verification and tests constraint satisfaction.

→ Full documentation

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🚀 Quick Start

Installation

pip install datasets

Loading the Dataset

from datasets import load_dataset

# Load a specific puzzle
dataset = load_dataset("gmannem/RecurrReason", "block_world")

# Access splits
train_data = dataset["train"]  # N=1-7
test_data = dataset["test"]    # N=8-10 (OOD)

# Iterate over examples
for example in train_data:
    print(f"Difficulty N={example['N']}")
    print(f"Current state: {example['current_state']}")
    print(f"Next state: {example['next_state']}")
    print(f"Move: {example['move']}")
    print("---")
    break

Loading All Puzzles

from datasets import load_dataset

puzzles = ["block_world", "checkers_jumping", "tower_of_hanoi", "river_crossing"]

datasets = {
    puzzle: load_dataset("gmannem/RecurrReason", puzzle)
    for puzzle in puzzles
}

# Access specific puzzle
bw_train = datasets["block_world"]["train"]

Example: Evaluating a Model

from datasets import load_dataset

# Load test data (OOD, N=8-10)
test_data = load_dataset("gmannem/RecurrReason", "block_world", split="test")

def evaluate_model(model, test_data):
    """
    Evaluate model on RecurrReason benchmark.
    
    Metrics:
    - Success rate: % of puzzles solved correctly
    - Move validity: % of generated moves that are legal
    - Optimality gap: (model_length - optimal_length) / optimal_length
    """
    success_count = 0
    
    for example in test_data:
        # Your model prediction logic here
        predicted_next_state = model.predict(
            current_state=example['current_state'],
            goal_state=example['goal_state']
        )
        
        # Check if prediction matches ground truth
        if predicted_next_state == example['next_state']:
            success_count += 1
    
    success_rate = success_count / len(test_data)
    print(f"Success Rate: {success_rate:.2%}")
    
    return success_rate

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📄 Paper & Code

"Recurrent Reasoning on Symbolic Puzzles with Sequence Models"
Gowrav Mannem, Chowdhury Marzia Mahjabin, Jason Chen, Shivank Garg, Kevin Zhu
ICLR 2026 Workshop on Logical Reasoning of Large Language Models

🔗 Read on OpenReview

📄 PDF

🔗 GitHub Repository

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📖 Citation

If you use RecurrReason in your research, please cite the following papers. This benchmark extends the puzzles introduced by Shojaee et al. (2025) with BFS-optimal trajectories, permutation augmentations, and systematic difficulty scaling.

@inproceedings{mannem2026recurrent,
  title={Recurrent Reasoning on Symbolic Puzzles with Sequence Models},
  author={Gowrav Mannem and Chowdhury Marzia Mahjabin and Jason Chen and Shivank Garg and Kevin Zhu},
  booktitle={ICLR 2026 Workshop on Logical Reasoning of Large Language Models},
  year={2026},
  url={https://openreview.net/forum?id=ErgAON9dOW}
}
@article{shojaee2025illusion,
  title={The illusion of thinking: Understanding the strengths and limitations of reasoning models via the lens of problem complexity},
  author={Shojaee, Parshin and Mirzadeh, Iman and Alizadeh, Keivan and Horton, Maxwell and Bengio, Samy and Farajtabar, Mehrdad},
  journal={arXiv preprint arXiv:2506.06941},
  year={2025}
}

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📜 License

This dataset is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

You are free to:

• Share — copy and redistribute the dataset
• Adapt — remix, transform, and build upon the dataset
• For any purpose, even commercially

Under the following terms:

• Attribution — You must give appropriate credit by citing our paper

Full license text: https://creativecommons.org/licenses/by/4.0/

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🤝 Contributing

Found an issue or have suggestions? Please:

1. Open an issue on GitHub
2. Use the "Discussions" tab on HuggingFace
3. Contact us at: gowravmannem@gmail.com

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