statement
stringlengths 118
1.2k
| solution
stringlengths 229
4.09k
| answer
int64 1
310M
| grade
float64 0
1
| model_solution_0
stringlengths 6k
159k
| model_solution_1
stringlengths 5.03k
126k
| model_solution_2
stringlengths 5.18k
119k
| model_solution_3
stringlengths 12.4k
115k
| model_solution_4
stringlengths 5.23k
111k
| model_solution_5
stringlengths 3.49k
124k
| model_solution_6
stringlengths 12.5k
134k
| model_solution_7
stringlengths 6.04k
127k
|
|---|---|---|---|---|---|---|---|---|---|---|---|
"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)
|
"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
| 0.625
| "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)
|
"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)
|
"Let \\( \\triangle ABC \\) be a triangle with \\( BC = 2007 \\), \\( CA = 2008 \\), \\( AB = 2009 \(...TRUNCATED)
| "Let line \\( AD \\) meet \\( \\omega \\) again at \\( H \\). Since \\( AF \\) and \\( AE \\) are ta(...TRUNCATED)
| 2,014,024
| 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)
|
"Let \\( G, A_{1}, A_{2}, A_{3}, A_{4}, B_{1}, B_{2}, B_{3}, B_{4}, B_{5} \\) be ten points on a cir(...TRUNCATED)
| "Note that \\( G B_{3} \\) is a diameter of the circle. As a result, \\( A_{2}, A_{3} \\) are symmet(...TRUNCATED)
| 12
| 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)
|
"At a certain college, there are $10$ clubs and some number of students. For any two different stude(...TRUNCATED)
| "Let \\( C \\) be the set of clubs; each student then corresponds to a subset of \\( C \\) (the club(...TRUNCATED)
| 513
| 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)
|
"Let \\( x_{1}, x_{2}, \\ldots, x_{2022} \\) be nonzero real numbers. Suppose that \\( x_{k}+\\frac{(...TRUNCATED)
| "Let the answer be \\( M \\). If \\( M > 1011 \\), there would exist two consecutive positive terms (...TRUNCATED)
| 1,010
| 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)
|
"Compute \\(\\arctan \\left(\\tan 65^{\\circ}-2 \\tan 40^{\\circ}\\right)\\). (Express your answer i(...TRUNCATED)
| "First Solution: We have\n\\[\n\\tan 65^{\\circ}-2 \\tan 40^{\\circ}=\\cot 25^{\\circ}-2 \\cot 50^{\(...TRUNCATED)
| 25
| 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)
|
"Rectangle \\(ABCD\\) has sides in the ratio of \\(\\sqrt{2}\\) to \\(1\\). If \\(\\triangle DEC\\) (...TRUNCATED)
| "Since \\(\\triangle DEC\\) is an isosceles right triangle, we have \\(ED = CD = \\sqrt{2} \\cdot AD(...TRUNCATED)
| 135
| 0.875
| "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)
|
"Bassanio has three red coins, four yellow coins, and five blue coins. At any point, he may give Shy(...TRUNCATED)
| "Let \\( r, y, b \\) denote the numbers of red, yellow, and blue coins respectively. Note that each (...TRUNCATED)
| 7
| 0.875
| "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)
|
End of preview. Expand
in Data Studio
README.md exists but content is empty.
- Downloads last month
- 6