MathDB

10.3

Part of 2009 All-Russian Olympiad Regional Round

Problems(1)

2 sets of 17 coines, 5 fakes

Source: All-Russian MO 2009 Regional 10. 3

8/27/2024
Kostya had two sets of 1717 coins: in one set all the coins were real, and in the other set there were exactly 55 fakes (all the coins look the same; all real coins weigh the same, all fake coins also weigh the same, but it is unknown lighter or heavier than real ones). Kostya gave away one of the sets friend, and subsequently forgot which of the two sets had stayed. With the help of two weighings, can Kostya on a cup scale without weights, find out which of the two did he give away the sets?
combinatoricsweights