prompt list | ground_truth string |
|---|---|
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.91 cm |
[
{
"content": "Two noncongruent integer-sided isosceles triangles have the same perimeter and the same area. The ratio of the lengths of the bases of the two triangles is $8: 7$. Find the minimum possible value of their common perimeter.",
"role": "user"
}
] | 676 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.518e-3 g/L |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.29 |
[
{
"content": "Let $I$ be an ideal of a Noetherian ring $R$. Determine whether there exists a positive integer $n$ such that $(\\sqrt{I})^n \\subseteq I$. Provide a proof or counterexample.",
"role": "user"
}
] | Yes |
[
{
"content": "Consider smooth vector bundles \\( \\pi_{1} : E_{1} \\to M \\) and \\( \\pi_{2} : E_{2} \\to M \\) over a smooth manifold \\( M \\). Let \\( T : \\Gamma(E_{1}) \\to \\Gamma(E_{2}) \\) be a map from the smooth sections of \\( E_{1} \\) to the smooth sections of \\( E_{2} \\). If \\( T \\) is \\( \\... | No |
[
{
"content": "Let $A$ be a bounded self-adjoint operator on a Hilbert space $\\mathcal{H}$. Assume that $A^2 \\leq A$, meaning $\\langle A^2v, v \\rangle \\leq \\langle Av, v \\rangle$ for all $v \\in \\mathcal{H}$. Prove or disprove that $0 \\leq A \\leq 1$, meaning $0 \\leq \\langle Av, v \\rangle \\leq \\lan... | 0 \leq A \leq 1 |
[
{
"content": "Find the remainder when $2^{1990}$ is divided by $1990$.",
"role": "user"
}
] | 1024 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | BaCl_2+(NH_4)_2CO_3 -> BaCO_3+2NH_4Cl |
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