100 diamonds, 50 genuine and 50 false, expert tells a number in every 2
Source: Czech and Slovak Olympiad 2017, National Round, III A p1
February 2, 2020
combinatoricsgamegame strategy
Problem Statement
There are diamonds on the pile, of which are genuine and false. We invited a peculiar expert who alone can recognize which are which. Every time we show him some three diamonds, he would pick two and tell (truthfully) how many of them are genuine . Decide whether we can surely detect all genuine diamonds regardless how the expert chooses the pairs to be considered.