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23 Boxes

Source: ToT - 2001 Fall Senior A-Level #6

August 17, 2011
inductioncombinatorics unsolvedcombinatorics

Problem Statement

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?
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