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Problem of the Week 1252

Equal Weight

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Suppose 13 coins have the property that whenever one is removed, the others can be divided into two groups of 6 having equal total weight.

Must all the coins have the same weight?

Source: The classic book, The USSR Problem Book by Shklarsky, Chentov, and Yaglom, Freeman, 1962.

Also in Peter Winkler, Mathematical Mindbenders, AK Peters, 2007, p. 23.

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15 November 2017