statement stringlengths 40 1.3k | solution stringlengths 56 6.9k | answer int64 0 310M | grade float64 0 1 | model_solution_0 stringlengths 3.45k 88.8k | model_solution_1 stringlengths 2.54k 88.9k | model_solution_2 stringlengths 3.04k 87.2k | model_solution_3 stringlengths 3.06k 90.3k | model_solution_4 stringlengths 3.31k 89.1k | model_solution_5 stringlengths 3.27k 90.6k | model_solution_6 stringlengths 3.12k 88.7k | model_solution_7 stringlengths 3.29k 92k |
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"How many ways are there for Nick to travel from \\((0,0)\\) to \\((16,16)\\) in the coordinate plan(...TRUNCATED) | "This condition is equivalent to the first and last step being in different directions, as if you sw(...TRUNCATED) | 310,235,040 | 1 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) |
"Regular hexagon \\(A B C D E F\\) has side length \\(1\\). Let \\(H\\) be the intersection point of(...TRUNCATED) | "Let \\(O\\) be the center of the circle through \\(D, F\\), and \\(H\\). By considering the geometr(...TRUNCATED) | 7 | 0 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) |
"An evil witch is making a potion to poison the people of PUMAClandia. In order for the potion to wo(...TRUNCATED) | "To solve this problem, we need to determine the number of ways to distribute the ingredients such t(...TRUNCATED) | 1,011 | 0 | "Okay, let's try to figure out this problem step by step. First, let's list out the constraints and (...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) |
"Let \\(ABCD\\) and \\(AEFG\\) be unit squares such that the area of their intersection is \\(\\frac(...TRUNCATED) | "Suppose the two squares intersect at a point \\(X \\neq A\\). If \\(\\mathcal{S}\\) is the region f(...TRUNCATED) | 4,840 | 0 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) |
"(b) Let \\( A = \\{V, W, X, Y, Z, v, w, x, y, z\\} \\). Find the number of subsets of the 2-configu(...TRUNCATED) | "Solution: No more than two of the pairs \\(\\{v, x\\}, \\{v, y\\}, \\{w, y\\}, \\{w, z\\}, \\{x, z\(...TRUNCATED) | 6 | 0 | "Okay, let's try to figure out this problem step by step. First, let's make sure I understand the pr(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) |
"$A_{1} A_{2} A_{3} A_{4}$ is a cyclic quadrilateral inscribed in circle $\\Omega$, with side length(...TRUNCATED) | "First, we claim that the points $P_{i}$ all lie on a circle. To show this, we first claim that $P_{(...TRUNCATED) | 784 | 0 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) |
"Let \\( \\triangle ABC \\) be an obtuse triangle with circumcenter \\( O \\) such that \\( \\angle (...TRUNCATED) | "Let the radius of the circumcircle of \\( \\triangle ABC \\) be \\( r \\).\n\n\\[\n\\begin{align*}\(...TRUNCATED) | 35 | 0.375 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) |
"It is possible to show that, given any real \\( M \\), there exists a positive integer \\( k \\) la(...TRUNCATED) | "Solution: Note that \\(\\frac{1}{n+1} + \\frac{1}{n+2} + \\ldots + \\frac{1}{2n} > \\frac{1}{2n} + (...TRUNCATED) | 256 | 0 | "Okay, let's try to figure out this problem. The question is asking for a value of \\( k \\) such th(...TRUNCATED) | "Okay, let's see. The problem is about the harmonic series, which we know diverges, so for any M, th(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "Okay, let's try to figure out this problem. So, the question is about the harmonic series, which we(...TRUNCATED) | "Okay, let's see. The problem is about finding a positive integer \\( k \\) such that the sum of the(...TRUNCATED) | "Okay, let's see. The problem is about the harmonic series, which we know diverges, so for any M, th(...TRUNCATED) | "Okay, let's try to figure out this problem. So, we need to find a positive integer \\( k \\) such t(...TRUNCATED) | "Okay, let's try to figure out this problem. The question is asking for a value of k such that the s(...TRUNCATED) |
"Problem: What is the smallest positive integer representable as the sum of the cubes of three posit(...TRUNCATED) | "Solution: Let this smallest positive integer be represented as \\(a^{3}+b^{3}+c^{3}=d^{3}+e^{3}+f^{(...TRUNCATED) | 251 | 1 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) |
"Call a positive integer \\( n \\) quixotic if the value of \n\n\\[ \n\\operatorname{lcm}(1,2,3, \(...TRUNCATED) | "Let \\( L = \\operatorname{lcm}(1,2,3, \\ldots, n) \\), and let \\( E = L\\left(1+\\frac{1}{2}+\\fr(...TRUNCATED) | 573 | 0 | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) |
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