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stringlengths 1
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stringlengths 68
7.49k
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64
| rewards
listlengths 64
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float64 0
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"In how many distinct ways can I arrange my six keys on a keychain, if I want to put my house key ne(...TRUNCATED) |
24
| "<|im_start|>user\nIn how many distinct ways can I arrange my six keys on a keychain, if I want to p(...TRUNCATED) | ["We are asked to find the number of **distinct arrangements** of **six keys** on a **keychain**, wi(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0 |
"Pentagon $ABCDE$ is inscribed in a circle such that $ACDE$ is a square with area $12$. Determine th(...TRUNCATED) |
9 + 3\sqrt{2}
| "<|im_start|>user\nPentagon $ABCDE$ is inscribed in a circle such that $ACDE$ is a square with area (...TRUNCATED) | ["We are given that pentagon $ABCDE$ is inscribed in a circle, and that quadrilateral $ACDE$ is a **(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | 0.96875 |
"Rectangle \\( EFGH \\) is 10 cm by 6 cm. \\( P \\) is the midpoint of \\( \\overline{EF} \\), and \(...TRUNCATED) |
30
| "<|im_start|>user\nRectangle \\( EFGH \\) is 10 cm by 6 cm. \\( P \\) is the midpoint of \\( \\overl(...TRUNCATED) | ["We are given a rectangle $ EFGH $ with dimensions:\n\n- Length = 10 cm (let鈥檚 assume $ EF = 10 $(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | 1 |
"Representing August 12, 2018, with eight digits is $12-08-2018$, where each digit appears exactly t(...TRUNCATED) |
6
| "<|im_start|>user\nRepresenting August 12, 2018, with eight digits is $12-08-2018$, where each digit(...TRUNCATED) | ["We are given that **August 12, 2018**, is written in the format **12-08-2018**, which uses **eight(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0 |
"Two individuals were sitting on a log, one taller and the other shorter. The shorter one is the son(...TRUNCATED) |
1
| "<|im_start|>user\nTwo individuals were sitting on a log, one taller and the other shorter. The shor(...TRUNCATED) | ["This riddle plays on assumptions about family relationships.\n\n**Riddle:** \n*Two individuals we(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0 |
"Let \\( ABC \\) be a triangle where \\(\\angle BCA = 90^\\circ\\), and let \\(D\\) be the foot of t(...TRUNCATED) |
MK=ML
| "<|im_start|>user\nLet \\( ABC \\) be a triangle where \\(\\angle BCA = 90^\\circ\\), and let \\(D\\(...TRUNCATED) | ["We are given a right triangle $ \\triangle ABC $ with $ \\angle BCA = 90^\\circ $, and $ D $ is th(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0.03125 |
Find all prime numbers \( p \) such that \( p^2 + 2007p - 1 \) is prime as well.
|
3
| "<|im_start|>user\nFind all prime numbers \\( p \\) such that \\( p^2 + 2007p - 1 \\) is prime as we(...TRUNCATED) | ["We are given a problem:\n\n**Find all prime numbers $ p $ such that $ p^2 + 2007p - 1 $ is also pr(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | 1 |
Which of the following is not the sum of two primes?
A) 5
B) 7
C) 9
D) 11
E) 13
|
11
| "<|im_start|>user\nWhich of the following is not the sum of two primes?\nA) 5\nB) 7\nC) 9\nD) 11\nE)(...TRUNCATED) | ["We are asked to determine which of the following numbers **is not** the sum of two prime numbers:\(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | 0.96875 |
"Given a triangle $\\triangle ABC$ with sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$(...TRUNCATED) |
\frac {15 \sqrt {7}}{4}
| "<|im_start|>user\nGiven a triangle $\\triangle ABC$ with sides $a$, $b$, and $c$ opposite to angles(...TRUNCATED) | ["We are given a triangle $ \\triangle ABC $ with:\n\n- $ \\cos A = \\frac{3}{4} $\n- $ \\cos C = \\(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0(...TRUNCATED) | 0.890625 |
"In parallelogram $ABCD$, diagonal $BD$ is equal to 2, angle $C$ is $45^\\circ$, and line $CD$ is ta(...TRUNCATED) |
4
| "<|im_start|>user\nIn parallelogram $ABCD$, diagonal $BD$ is equal to 2, angle $C$ is $45^\\circ$, a(...TRUNCATED) | ["We are given a parallelogram $ABCD$ with the following properties:\n\n- Diagonal $BD = 2$\n- $\\an(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0(...TRUNCATED) | 0.9375 |
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