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Cutting a piece of cheese in a given ratio...

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February 7, 2011
rationumber theory unsolvednumber theory

Problem Statement

Alex has a piece of cheese. He chooses a positive number a1a\neq 1 and cuts the piece into several pieces one by one. Every time he chooses a piece and cuts it in the same ratio 1:a.1:a. His goal is to divide the cheese into two piles of equal masses. Can he do it?