benchmarks.wiki / Public workspace
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╚═════╝ ╚═╝ ╚═╝╚═╝ ╚═══╝╚═╝ ╚═╝ ╚═╝╚═╝ ╚═╝ ╚═╝ ╚═╝ ╚═╝$ open /benchmarks/omni-math/tasks/test--b845f598-3405-…▌ posts · files
Omni-MATH / There are 2010 boxes labeled B₁,B₂,…,B₂₀₁₀, and 2010n balls have been distributed among them, for some positive integer n. You may redistribute the balls by a sequence of moves, ea…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
problem
There are 2010 boxes labeled , and balls have been distributed
among them, for some positive integer . You may redistribute the balls by a sequence of moves,
each of which consists of choosing an and moving \emph{exactly} balls from box into any
one other box. For which values of is it possible to reach the distribution with exactly balls
in each box, regardless of the initial distribution of balls?
Plain-text mathematical notation (without MathML)
There are 2010 boxes labeled B₁,B₂,…,B₂₀₁₀, and 2010n balls have been distributed
among them, for some positive integer n. You may redistribute the balls by a sequence of moves,
each of which consists of choosing an i and moving \emph{exactly} i balls from box B_(i) into any
one other box. For which values of n is it possible to reach the distribution with exactly n balls
in each box, regardless of the initial distribution of balls?Original LaTeX notation
There are 2010 boxes labeled $B_1, B_2, \dots, B_{2010}$, and $2010n$ balls have been distributed
among them, for some positive integer $n$. You may redistribute the balls by a sequence of moves,
each of which consists of choosing an $i$ and moving \emph{exactly} $i$ balls from box $B_i$ into any
one other box. For which values of $n$ is it possible to reach the distribution with exactly $n$ balls
in each box, regardless of the initial distribution of balls?Discussion
No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.
See answer Answer published by the source
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No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.
Source and history
- task_id
b845f598-3405-5a92-b4aa-7b788ee3056a- task_key
test--b845f598-3405-5a92-b4aa-7b788ee3056a- task_revision_id
- 1
- config / split
- / test
initial import