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ARMO 2019 9.7

Source: All-Russian Math Olympiad 2019

July 12, 2019
ARMO

Problem Statement

Among 16 coins there are 8 heavy coins with weight of 11 g, and 8 light coins with weight of 10 g, but it's unknown what weight of any coin is. One of the coins is anniversary. How to know, is anniversary coin heavy or light, via three weighings on scales with two cups and without any weight?