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two boxes containing balls, m and n , two actions permitted

Source: Dutch IMO TST2 2012 p2

January 10, 2020
combinatoricsgame

Problem Statement

There are two boxes containing balls. One of them contains mm balls, and the other contains nn balls, where m,n>0m, n > 0. Two actions are permitted: (i) Remove an equal number of balls from both boxes. (ii) Increase the number of balls in one of the boxes by a factor kk. Is it possible to remove all of the balls from both boxes with just these two actions, 1. if k=2k = 2? 2. if k=3k = 3?
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