benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / In a row are 23 boxes such that for 1≤k≤23, there is a box containing exactly k balls. In one move, we can double the number of balls in any box by taking balls from another box wh…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

In a row are 23 boxes such that for 1≤k≤231\le k \le 23, there is a box containing exactly kk balls. In one move, we can double the number of balls in any box by taking balls from another box which has more. Is it always possible to end up with exactly kk balls in the kk-th box for 1≤k≤231\le k\le 23?
Plain-text mathematical notation (without MathML)
In a row are 23 boxes such that for 1≤k≤23, there is a box containing exactly k balls.  In one move, we can double the number of balls in any box by taking balls from another box which has more.  Is it always possible to end up with exactly k balls in the k-th box for 1≤k≤23?
Original LaTeX notation
In a row are 23 boxes such that for $1\le k \le 23$, there is a box containing exactly $k$ balls.  In one move, we can double the number of balls in any box by taking balls from another box which has more.  Is it always possible to end up with exactly $k$ balls in the $k$-th box for $1\le k\le 23$?

Discussion

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

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

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
daa7d30c-1e79-5b4c-8641-2e18bc928164
task_key
test--daa7d30c-1e79-5b4c-8641-2e18bc928164
task_revision_id
1
config / split
/ test

Official source

initial import