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olympiadbench: rebuild from official Hothan/OlympiadBench

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Source: Hothan/OlympiadBench @ 91184b52131e7fc9455fef848035173aea8cc01a, config OE_TO_maths_en_COMP.
Previous RLLab/eval-set revision: b0c72eb18091847ae39aa73de37af1c44af4c6a3

The previous rows were a copy of knoveleng/OlympiadBench, an older snapshot:
- 15 ARML relay problems read "Let $T=T N Y W R$" (the number you will receive) and could not be solved. Upstream now states T; the final answers are unchanged.
- 1 problem (official id 1965, a prose answer that cannot be graded automatically) was removed upstream and is dropped here.
- 1 gold follows upstream, which moved the degree sign to its `unit` field.

Format is unchanged: `problem` = official question + the step-by-step / \boxed{} instruction, `solution` = "\boxed{" + final_answer without "$" + "}".

Diff against the previous revision (675 -> 674 rows):
- rows unchanged: 658
- rows whose gold was rewritten (same problem): 1
- problems added: 15
- problems removed: 16
- order of the remaining rows kept: yes

Gold rewrites (contents of \boxed{...}):
- 44^{\circ} -> 44

Added problems:
- Let T be any number you want. Compute $2^{\log _{T} 8}-8^{\log _{T} 2}$.
- Let $T=0$. At some point during a given week, a law enforcement officer had issued $T+2$ traffic ...
- Let $T=15$. In parallelogram $A R M L$, points $P$ and $Q$ trisect $\overline{A R}$ and points $W...
- Let $T=7$. Compute the number of positive perfect cubes that are divisors of $(T+10) !$.
- Let $T=36$. The graph of $y=x^{2}+2 x-T$ intersects the $x$-axis at points $A$ and $M$, which are...
- Let $T=184$. A group of $n$ friends goes camping; two of them are selected to set up the campsite...
- Let $T=8$. The parabola $y=x^{2}+T x$ is tangent to the parabola $y=-(x-2 T)^{2}+b$. Compute $b$.
- Let $T=19$. The first two terms of a sequence are $a_{1}=3 / 5$ and $a_{2}=4 / 5$. For $n>2$, if ...
- Let $T=17$. A regular $n$-gon has exactly $T$ more diagonals than a regular $(n-1)$-gon. Compute ...
- Let $T=27/2$. The sequence $a_{1}, a_{2}, a_{3}, \ldots$, is arithmetic with $a_{16}=13$ and $a_{...
- Let $T=114$. A rectangular prism has a length of 1 , a width of 3 , a height of $h$, and has a to...
- Let $T=\frac{1}{2}$. Compute the largest real solution $x$ to $(\log x)^{2}-\log \sqrt{x}=T$.
- Let $T=10$. Kay has $T+1$ different colors of fingernail polish. Compute the number of ways that ...
- Let $T=4$ and let $k=21+2 T$. Compute the largest integer $n$ such that $2 n^{2}-k n+77$ is a pos...
- Let $T=12$. In triangle $A B C, B C=T$ and $\mathrm{m} \angle B=30^{\circ}$. Compute the number o...

Removed problems:
- For every positive integer $n$ with prime factorization $n=\prod_{i=1}^{k} p_{i}^{\alpha_{i}}$, d...
- Let $T=T N Y W R$. Compute $2^{\log _{T} 8}-8^{\log _{T} 2}$.
- Let $T=T N Y W R$. At some point during a given week, a law enforcement officer had issued $T+2$ ...
- $\quad$ Let $T=T N Y W R$. In parallelogram $A R M L$, points $P$ and $Q$ trisect $\overline{A R}...
- Let $T=T N Y W R$. Compute the number of positive perfect cubes that are divisors of $(T+10) !$.
- Let $T=T N Y W R$. The graph of $y=x^{2}+2 x-T$ intersects the $x$-axis at points $A$ and $M$, wh...
- Let $T=T N Y W R$. A group of $n$ friends goes camping; two of them are selected to set up the ca...
- Let $T=T N Y W R$. The parabola $y=x^{2}+T x$ is tangent to the parabola $y=-(x-2 T)^{2}+b$. Comp...
- Let $T=T N Y W R$. The first two terms of a sequence are $a_{1}=3 / 5$ and $a_{2}=4 / 5$. For $n>...
- Let $T=T N Y W R$. A regular $n$-gon has exactly $T$ more diagonals than a regular $(n-1)$-gon. C...
- Let $T=T N Y W R$. The sequence $a_{1}, a_{2}, a_{3}, \ldots$, is arithmetic with $a_{16}=13$ and...
- Let $T=T N Y W R$. A rectangular prism has a length of 1 , a width of 3 , a height of $h$, and ha...
- Let $T=T N Y W R$. Compute the largest real solution $x$ to $(\log x)^{2}-\log \sqrt{x}=T$.
- Let $T=T N Y W R$. Kay has $T+1$ different colors of fingernail polish. Compute the number of way...
- Let $T=T N Y W R$ and let $k=21+2 T$. Compute the largest integer $n$ such that $2 n^{2}-k n+77$ ...
- Let $T=T N Y W R$. In triangle $A B C, B C=T$ and $\mathrm{m} \angle B=30^{\circ}$. Compute the n...

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