benchmarks.wiki / Public workspace
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Omni-MATH / Omkar, …x>0 pints of soup for dinner. Omkar always takes 1 pint of soup (unless the amount left is less than one pint, in which case he simply takes all the remaining soup). Krit …
Problem
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problem
Omkar, \mathrm{Krit}_{1}, \mathrm{Krit}_{2}, and \mathrm{Krit}_{3} are sharing pints of soup for dinner. Omkar always takes 1 pint of soup (unless the amount left is less than one pint, in which case he simply takes all the remaining soup). Krit
$_{1}$ always takes \frac{1}{6}{ }_{2} of what is left, and \mathrm{Krit}_{3} of what is left. They take soup in the order of Omkar, \mathrm{Krit}_{1}, \mathrm{Krit}_{2}, \mathrm{Krit}_{3}x$ for which everyone gets the same amount of soup.Plain-text mathematical notation (without MathML)
Omkar, \mathrm{Krit}_{1}, \mathrm{Krit}_{2}, and \mathrm{Krit}_{3} are sharing x>0 pints of soup for dinner. Omkar always takes 1 pint of soup (unless the amount left is less than one pint, in which case he simply takes all the remaining soup). Krit $_{1}$ always takes \frac{1}{6}ofwhatisleft,Krit{ }_{2}alwaystakes(1)/(5) of what is left, and \mathrm{Krit}_{3}alwaystakes(1)/(4) of what is left. They take soup in the order of Omkar, \mathrm{Krit}_{1}, \mathrm{Krit}_{2}, \mathrm{Krit}_{3},andthencyclethroughthisorderuntilnosoupremains.Findallx$ for which everyone gets the same amount of soup.Original LaTeX notation
Omkar, \mathrm{Krit}_{1}, \mathrm{Krit}_{2}, and \mathrm{Krit}_{3} are sharing $x>0$ pints of soup for dinner. Omkar always takes 1 pint of soup (unless the amount left is less than one pint, in which case he simply takes all the remaining soup). Krit $_{1}$ always takes \frac{1}{6}$ of what is left, Krit ${ }_{2}$ always takes \frac{1}{5}$ of what is left, and \mathrm{Krit}_{3}$ always takes \frac{1}{4}$ of what is left. They take soup in the order of Omkar, \mathrm{Krit}_{1}, \mathrm{Krit}_{2}, \mathrm{Krit}_{3}$, and then cycle through this order until no soup remains. Find all $x$ for which everyone gets the same amount of soup.Discussion
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- task_id
ebefa197-98e9-5cd5-9894-2fa6d63516f9- task_key
test--ebefa197-98e9-5cd5-9894-2fa6d63516f9- task_revision_id
- 1
- config / split
- / test
initial import