question stringlengths 326 14.9k | answer stringlengths 1 664 | taskname stringclasses 36
values | doc_id int64 0 670 | o3-mini-high_correct bool 2
classes | o4-mini-high_correct bool 2
classes |
|---|---|---|---|---|---|
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In each square of a garden shaped ... | ["2271380"] | olympiadbench_OE_TO_maths_en_COMP | 83 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Find all triples of positive integ... | ["$(2,2,2),(3,4,3)$"] | olympiadbench_OE_TO_maths_en_COMP | 89 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $a_{0}, a_{1}, a_{2}, \ldots$ ... | ["$\\frac{2016}{2017^{2}}$"] | olympiadbench_OE_TO_maths_en_COMP | 91 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Find the maximal value of
$$
S=\s... | ["$\\frac{8}{\\sqrt[3]{7}}$"] | olympiadbench_OE_TO_maths_en_COMP | 92 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In the plane, 2013 red points and ... | ["2013"] | olympiadbench_OE_TO_maths_en_COMP | 97 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: For any integer $n \geq 2$, let $N... | ["$N(n)=\\left\\lfloor\\frac{2 n}{3}\\right\\rfloor+1$"] | olympiadbench_OE_TO_maths_en_COMP | 101 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $n \geq 1$ be an integer. What... | ["$\\lfloor\\frac{2 n-1}{5}\\rfloor$"] | olympiadbench_OE_TO_maths_en_COMP | 109 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Find all triples $(x, y, z)$ of po... | ["$(2,251,252)$"] | olympiadbench_OE_TO_maths_en_COMP | 112 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Find the smallest positive integer... | ["$k=3$"] | olympiadbench_OE_TO_maths_en_COMP | 115 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $m$ be a positive integer. Con... | ["$6m$"] | olympiadbench_OE_TO_maths_en_COMP | 116 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: The $n$ contestants of an EGMO are... | ["$2^{n}-n-1$"] | olympiadbench_OE_TO_maths_en_COMP | 118 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $n$ be a positive integer. Dom... | ["$\\frac{n(n+1)}{2}$"] | olympiadbench_OE_TO_maths_en_COMP | 120 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $k$ be a positive integer. Lex... | ["$2^{k-1}$"] | olympiadbench_OE_TO_maths_en_COMP | 123 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Square $O P Q R$ has vertices $O(0... | ["$\\frac{32}{9}$,$\\frac{1}{2}$"] | olympiadbench_OE_TO_maths_en_COMP | 137 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: For some real numbers $m$ and $n$,... | ["1,-1,7,-7"] | olympiadbench_OE_TO_maths_en_COMP | 153 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Suppose that $f(a)=2 a^{2}-3 a+1$ ... | ["$\\frac{1}{6} \\pi, \\frac{5}{6} \\pi, \\frac{1}{4} \\pi, \\frac{3}{4} \\pi$"] | olympiadbench_OE_TO_maths_en_COMP | 158 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Suppose that $a=5$ and $b=4$. Dete... | ["$(3,2),(-3,2),(3,-2),(-3,-2)$"] | olympiadbench_OE_TO_maths_en_COMP | 159 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A Skolem sequence of order $n$ is ... | ["(7,5,1,1,9,3,5,7,3,8,6,4,2,9,2,4,6,8)"] | olympiadbench_OE_TO_maths_en_COMP | 169 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A chemist has three bottles, each ... | ["17.5%"] | olympiadbench_OE_TO_maths_en_COMP | 187 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Determine all real values of $x$ f... | ["$1$,$\\frac{3 + \\sqrt{21}}{2}$,$\\frac{3 - \\sqrt{21}}{2}$"] | olympiadbench_OE_TO_maths_en_COMP | 205 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Determine all points $(x, y)$ wher... | ["$(1,0),(\\frac{1}{100},-8),(100,8)$"] | olympiadbench_OE_TO_maths_en_COMP | 206 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Determine all real values of $x$ f... | ["$[\\frac{1}{2}, 8]$"] | olympiadbench_OE_TO_maths_en_COMP | 220 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In an arithmetic sequence with 5 t... | ["-5,7"] | olympiadbench_OE_TO_maths_en_COMP | 225 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A positive integer $n$ is called "... | ["8,32,44,68,80"] | olympiadbench_OE_TO_maths_en_COMP | 243 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Determine all pairs $(a, b)$ of po... | ["$(1,1006),(3,331),(11,31)$"] | olympiadbench_OE_TO_maths_en_COMP | 247 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Determine all real values of $x$ s... | ["$0,-1,-\\frac{3}{2}$"] | olympiadbench_OE_TO_maths_en_COMP | 259 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: If $\log _{2} x,\left(1+\log _{4} ... | ["$64,\\frac{1}{4}$"] | olympiadbench_OE_TO_maths_en_COMP | 287 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: The populations of Alphaville and ... | ["4.2"] | olympiadbench_OE_TO_maths_en_COMP | 315 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: An integer-valued function $f$ is ... | ["136"] | olympiadbench_OE_TO_maths_en_COMP | 325 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A student computed the repeating d... | ["606"] | olympiadbench_OE_TO_maths_en_COMP | 336 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A point is selected at random from... | ["$(\\frac{1}{4}, \\frac{1}{27})$"] | olympiadbench_OE_TO_maths_en_COMP | 340 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $W=(0,0), A=(7,0), S=(7,1)$, a... | ["3432"] | olympiadbench_OE_TO_maths_en_COMP | 344 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $T=37$. A cube has edges of le... | ["8640"] | olympiadbench_OE_TO_maths_en_COMP | 378 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $A R M L$ be a trapezoid with ... | ["48"] | olympiadbench_OE_TO_maths_en_COMP | 386 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In right triangle $A B C$ with rig... | ["14"] | olympiadbench_OE_TO_maths_en_COMP | 395 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $S=\{1,2, \ldots, 20\}$, and l... | ["140"] | olympiadbench_OE_TO_maths_en_COMP | 397 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: The ARMLLexicon consists of 10 let... | ["99956"] | olympiadbench_OE_TO_maths_en_COMP | 416 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Circle $\omega$ is tangent to para... | ["$5 \\sqrt{10}$"] | olympiadbench_OE_TO_maths_en_COMP | 419 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $\mathcal{S}$ denote the set o... | ["46760"] | olympiadbench_OE_TO_maths_en_COMP | 421 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Suppose that noncongruent triangle... | ["$25 \\sqrt{3}$"] | olympiadbench_OE_TO_maths_en_COMP | 435 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: The mean, median, and unique mode ... | ["12"] | olympiadbench_OE_TO_maths_en_COMP | 436 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In quadrilateral $A B C D, \mathrm... | ["$\\sqrt{130}$"] | olympiadbench_OE_TO_maths_en_COMP | 438 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Three non-overlapping squares of p... | ["32"] | olympiadbench_OE_TO_maths_en_COMP | 455 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A circle with center $O$ and radiu... | ["$\\frac{\\sqrt{3}}{32}$"] | olympiadbench_OE_TO_maths_en_COMP | 456 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: If $n$ is a positive integer, then... | ["1510"] | olympiadbench_OE_TO_maths_en_COMP | 460 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In triangle $A B C, A B=B C$. A tr... | ["146"] | olympiadbench_OE_TO_maths_en_COMP | 463 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $T=11$. In ARMLvania, license ... | ["256"] | olympiadbench_OE_TO_maths_en_COMP | 468 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Compute the number of ordered pair... | ["81"] | olympiadbench_OE_TO_maths_en_COMP | 473 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: The graphs of $y=x^{2}-|x|-12$ and... | ["$10+2 \\sqrt{2}$"] | olympiadbench_OE_TO_maths_en_COMP | 476 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $A B C$ be a triangle with $\m... | ["6"] | olympiadbench_OE_TO_maths_en_COMP | 479 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Given that April $1^{\text {st }},... | ["2018"] | olympiadbench_OE_TO_maths_en_COMP | 493 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $k$ be the least common multip... | ["23"] | olympiadbench_OE_TO_maths_en_COMP | 499 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: If $6 \tan ^{-1} x+4 \tan ^{-1}(3 ... | ["$\\frac{15-8 \\sqrt{3}}{33}$"] | olympiadbench_OE_TO_maths_en_COMP | 503 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In $\triangle A B C, D$ is on $\ov... | ["3"] | olympiadbench_OE_TO_maths_en_COMP | 513 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: For a positive integer $n$, define... | ["9046"] | olympiadbench_OE_TO_maths_en_COMP | 522 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Points $P, Q, R$, and $S$ lie in t... | ["$2-\\sqrt{3}$"] | olympiadbench_OE_TO_maths_en_COMP | 539 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $\mathcal{R}$ denote the circu... | ["48"] | olympiadbench_OE_TO_maths_en_COMP | 541 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In square $A B C D$ with diagonal ... | ["$4-2 \\sqrt{3}$"] | olympiadbench_OE_TO_maths_en_COMP | 544 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: An integer $N$ is worth 1 point fo... | ["100337"] | olympiadbench_OE_TO_maths_en_COMP | 557 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Six solid regular tetrahedra are p... | ["$\\frac{\\sqrt{2}}{3}$"] | olympiadbench_OE_TO_maths_en_COMP | 561 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Derek starts at the point $(0,0)$,... | ["529"] | olympiadbench_OE_TO_maths_en_COMP | 562 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Each of the six faces of a cube is... | ["$\\frac{9}{32}$"] | olympiadbench_OE_TO_maths_en_COMP | 581 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Given that $a, b, c$, and $d$ are ... | ["2240"] | olympiadbench_OE_TO_maths_en_COMP | 586 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Let $T=67$. Rectangles $F A K E$ a... | ["262"] | olympiadbench_OE_TO_maths_en_COMP | 593 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Eight students attend a Harper Val... | ["12"] | olympiadbench_OE_TO_maths_en_COMP | 607 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In non-right triangle $A B C$, dis... | ["$\\frac{45}{2}$"] | olympiadbench_OE_TO_maths_en_COMP | 609 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Compute the least positive integer... | ["7986"] | olympiadbench_OE_TO_maths_en_COMP | 612 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Circle $\omega_{1}$ has center $O$... | ["$548 \\pi$"] | olympiadbench_OE_TO_maths_en_COMP | 640 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Some portions of the line $y=4 x$ ... | ["$\\frac{5 \\pi}{4} \\sqrt{17}$"] | olympiadbench_OE_TO_maths_en_COMP | 653 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In equilateral hexagon $A B C D E ... | ["$\\frac{9}{2}$"] | olympiadbench_OE_TO_maths_en_COMP | 654 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Given a regular 16-gon, extend thr... | ["11"] | olympiadbench_OE_TO_maths_en_COMP | 658 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Two square tiles of area 9 are pla... | ["$\\frac{5}{4}$"] | olympiadbench_OE_TO_maths_en_COMP | 659 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Inside a laboratory at room temper... | ["0.0320"] | olympiadbench_OE_TO_physics_en_COMP | 6 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A point charge $+q$ is placed a di... | ["0.916"] | olympiadbench_OE_TO_physics_en_COMP | 18 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Jerry spots a truckload of his fav... | ["10.9375"] | olympiadbench_OE_TO_physics_en_COMP | 19 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Consider an LC circuit with one in... | ["$11.892$"] | olympiadbench_OE_TO_physics_en_COMP | 20 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: What is the smallest number of $1 ... | ["5"] | olympiadbench_OE_TO_physics_en_COMP | 22 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A straight ladder $A B$ of mass $m... | ["$11.5$"] | olympiadbench_OE_TO_physics_en_COMP | 28 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Two Ladders Two straight ladders $... | ["$\\frac{2\\sqrt{5}}{3}$"] | olympiadbench_OE_TO_physics_en_COMP | 29 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Adithya is launching a package fro... | ["$7564$"] | olympiadbench_OE_TO_physics_en_COMP | 31 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A scientist is doing an experiment... | ["90"] | olympiadbench_OE_TO_physics_en_COMP | 35 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: For this problem, assume the Earth... | ["-2"] | olympiadbench_OE_TO_physics_en_COMP | 39 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Given vertically polarized light, ... | ["$\\cos ^{10}(\\frac{\\pi}{10})$"] | olympiadbench_OE_TO_physics_en_COMP | 41 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Two concentric isolated rings of r... | ["$2 \\pi \\sqrt{\\frac{10 \\ln (2)}{3 \\pi}}$"] | olympiadbench_OE_TO_physics_en_COMP | 48 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A table of unknown material has a ... | ["$18.71$"] | olympiadbench_OE_TO_physics_en_COMP | 49 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: In quantum mechanics, when calcula... | ["$0.0254$"] | olympiadbench_OE_TO_physics_en_COMP | 52 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Suppose we have a non-ideal gas, a... | ["$\\frac{7}{4}$"] | olympiadbench_OE_TO_physics_en_COMP | 56 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Follin is investigating the electr... | ["$0.0475$"] | olympiadbench_OE_TO_physics_en_COMP | 72 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: (a) What value of $\theta$ maximiz... | ["$\\frac{\\pi}{4}$"] | olympiadbench_OE_TO_physics_en_COMP | 82 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: (b) What value of $\theta$ maximiz... | ["$\\pi / 3$"] | olympiadbench_OE_TO_physics_en_COMP | 83 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: 2.3 The bubble is initially formed... | ["307.1"] | olympiadbench_OE_TO_physics_en_COMP | 99 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: A.2 The total energy of the 2-mass... | ["$A(\\mu, \\Omega, L)=\\frac{1}{2} \\mu L^{2} \\Omega^{2}$"] | olympiadbench_OE_TO_physics_en_COMP | 162 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: B.4 Using the information provided... | ["p=1"] | olympiadbench_OE_TO_physics_en_COMP | 166 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: ii. Assuming that the particle has... | ["$\\frac{F_{\\text {radiation }}}{F_{\\text {gravity }}}=\\frac{3 L_{\\odot}}{16 \\pi G c M_{\\odot} \\rho} \\frac{Q}{r}$"] | olympiadbench_OE_TO_physics_en_COMP | 218 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: 5. Calculate the velocity of the ... | ["$\\beta=\\tanh \\frac{g \\tau}{c}$"] | olympiadbench_OE_TO_physics_en_COMP | 229 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: 6. ( $\mathbf{0 . 4} \mathbf{~ p t... | ["$t=\\frac{c}{g} \\sinh \\frac{g \\tau}{c}$"] | olympiadbench_OE_TO_physics_en_COMP | 230 | true | false |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$.
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: 2. A uniform magnetic field $\bol... | ["$\\omega_{0}=\\gamma B_{0}$"] | olympiadbench_OE_TO_physics_en_COMP | 231 | false | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Assume all gases are perfect... | -1.5 | scibench | 9 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Assume all gases are perfect... | -114.40 | scibench | 22 | true | true |
Solve the following math problem step by step. Always conclude with:
Therefore, the final answer is: $\boxed{answer}$(unit).
Where [answer] is just the final number or LaTex expression that solves the problem. Note that the unit of the answers should not be included in \boxed{}
Problem: Assume all gases are perfect... | +17.7 | scibench | 46 | false | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.