statement stringlengths 40 1.3k | solution stringlengths 40 6.9k | answer int64 0 6.21B | grade float64 0 1 | model_solution_0 stringlengths 2.29k 173k | model_solution_1 stringlengths 2.66k 161k | model_solution_2 stringlengths 2.83k 148k | model_solution_3 stringlengths 2.24k 151k | model_solution_4 stringlengths 2.11k 173k | model_solution_5 stringlengths 2.76k 165k | model_solution_6 stringlengths 2.59k 150k | model_solution_7 stringlengths 2.15k 141k |
|---|---|---|---|---|---|---|---|---|---|---|---|
"Let \\(\\omega\\) be a circle of radius \\(6\\) with center \\(O\\). Let \\(AB\\) be a chord of \\((...TRUNCATED) | "It is easy to see, by the Pythagorean theorem, that \\(\\mathcal{L}(c)\\) for any \\(c\\) consists (...TRUNCATED) | 60 | 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) |
"In the future, MIT has attracted so many students that its buildings have become skyscrapers. Ben a(...TRUNCATED) | "Define the following lengths:\n\nNote that due to all the 3-4-5 triangles, we find \\(\\frac{x}{z}=(...TRUNCATED) | 740 | 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) |
"Hexagon \\(A B C D E F\\) has an inscribed circle \\(\\Omega\\) that is tangent to each of its side(...TRUNCATED) | "Let \\(r\\) denote the radius of \\(\\Omega\\), let \\(O\\) denote the center of \\(\\Omega\\), and(...TRUNCATED) | 36 | 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) |
"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) |
"A function \\( f:\\{1,2, \\ldots, n\\} \\rightarrow\\{1, \\ldots, m\\} \\) is multiplication-preser(...TRUNCATED) | "Since \\( f(1)^2 = f(1) \\), then \\( f(1) = 1 \\). We have that \\( f(2)^3 = f(8) \\leq 88 \\) and(...TRUNCATED) | 33 | 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) |
If \( x \) is a positive real number such that \((x^{2}-1)^{2}-1=9800\), compute \( x \). | "We have \\((x^{2}-1)^{2} = 9801\\), so \\(x^{2}-1 = \\pm 99\\). Since \\(x^{2}\\) cannot be negativ(...TRUNCATED) | 10 | 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) | "Okay, let's see. The problem is: If \\( x \\) is a positive real number such that \\( (x^{2} - 1)^{(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) | "Okay, let's see. I need to solve the equation \\((x^2 - 1)^2 - 1 = 9800\\) where \\(x\\) is a posit(...TRUNCATED) | "This is a complex or challenging question, and it is difficult to provide a direct and correct answ(...TRUNCATED) |
Find the smallest positive integer \( n \) such that \( n^{4}+(n+1)^{4} \) is composite. | "Solution: We need to find the smallest positive integer \\( n \\) such that \\( n^4 + (n+1)^4 \\) i(...TRUNCATED) | 5 | 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) |
"Find the largest integer \\( n \\), where \\( 2009^{n} \\) divides \\( 2008^{2009^{2010}} + 2010^{2(...TRUNCATED) | "Using the binomial theorem:\n\n\\[\n\\begin{gathered}\nA = (2009 - 1)^{2009^{2010}} = -1 + 2009 \\t(...TRUNCATED) | 2,009 | 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) |
"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 | "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
- 5