2022 / 2023 plates around a round table, 2 player game
Source: 2022 Saudi Arabia IMO TST 4.1
November 1, 2022
combinatoricsgamegame strategy
Problem Statement
There are a) , b) plates placed around a round table and on each of them there is one coin. Alice and Bob are playing a game that proceeds in rounds indefinitely as follows. In each round, Alice first chooses a plate on which there is at least one coin. Then Bob moves one coin from this plate to one of the two adjacent plates, chosen by him. Determine whether it is possible for Bob to select his moves so that, no matter how Alice selects her moves, there are never more than two coins on any plate.