difficulty stringclasses 30
values | source stringclasses 16
values | domain stringclasses 3
values | conversations listlengths 2 2 |
|---|---|---|---|
null | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | [
{
"from": "human",
"value": "Let \\(a, b, c\\) be reals satisfying \\(a^2 + b^2 + c^2 = 6\\). Calculate the maximum value of the expression \\((a-b)^3 + (b-c)(c-a)\\)."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I have this problem where I need to find the maximum value of the expression (a... |
null | nvidia/OpenScienceReasoning-2 | science | [
{
"from": "human",
"value": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhich of the following scheduling algorithms could potentially lead to starvation in a computer system?\nA: First-Come, First-Served (FCFS)\nB: Shortest Job First (SJF)\nC: Round Robi... |
null | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | [
{
"from": "human",
"value": "Let \\( G \\) be a simple graph on \\( n \\) vertices (\\( n > 3 \\)) with no vertex of degree \\( n-1 \\). Suppose that for any two vertices of \\( G \\), there is a unique vertex joined to both of them. Calculate the common degree of each vertex in \\( G \\)."
},
{
"fr... |
null | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | [
{
"from": "human",
"value": "Find all integers $(x, y, z)$ satisfying the equation $12^x + y^4 = 56^z$."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find all integer solutions (x, y, z) to the equation 12^x + y^4 = 56^z. Hmm, let's start by understanding the problem. All variables ... |
UNKNOWN_DIFFICULTY | nvidia/OpenCodeReasoning|aizu | code | [
{
"from": "human",
"value": "You survived several months of exam wars and were able to enter ICPC University on a sunny day. On the day of admission, there was an enthusiastic recruitment of circles on the campus of the university, and you received a large number of pamphlets and returned. When you return t... |
null | nvidia/OpenMathReasoning|aops_c6_high_school_olympiads | math | [
{
"from": "human",
"value": "In a convex quadrilateral \\(ABCD\\) with diagonals intersecting at point \\(S\\), given that \\(\\angle SAB = \\angle SBC = 30^\\circ\\) and \\(\\angle SCD = \\angle SDA = 45^\\circ\\), find the angle between the diagonals of the quadrilateral."
},
{
"from": "gpt",
... |
null | nvidia/OpenScienceReasoning-2 | science | [
{
"from": "human",
"value": "Solve the following problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( A = \\{1, 2, 3\\} \\) and \\( B = \\{a, b, c, d\\} \\). Consider the Cartesian product \\( A \\times B \\). How many subsets of \\( A \\times B \\) contain exactly one element... |
null | nvidia/OpenScienceReasoning-2 | science | [{"from":"human","value":"Solve the following problem. Make sure to put the answer (and only answer)(...TRUNCATED) |
null | nvidia/OpenScienceReasoning-2 | science | [{"from":"human","value":"Solve the following problem. Make sure to put the answer (and only answer)(...TRUNCATED) |
null | nvidia/OpenScienceReasoning-2 | science | [{"from":"human","value":"Solve the following problem. Make sure to put the answer (and only answer)(...TRUNCATED) |
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