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315 marbles divided into three piles of 81, 115 and 119

Source: Singapore Junior Math Olympiad 2019 2nd Round p2 SMO

March 26, 2020
combinatorics

Problem Statement

There are 315315 marbles divided into three piles of 81,11581, 115 and 119119. In each move Ah Meng can either merge several piles into a single pile or divide a pile with an even number of marbles into 22 equal piles. Can Ah Meng divide the marbles into 315315 piles, each with a single marble?
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