MathDB

1

Part of 2023 Czech and Slovak Olympiad III A.

Problems(1)

SKMO 2023 P1

Source: czechoslovak national mo round

4/4/2023
Alice and Bob are playing a game on a plane consisting of 7272 cells arranged in circle. At the beginning of the game, Bob places a stone on some of the cells. Then, in every round first Alice picks one empty cell and then Bob must move a stone from one of the two neighboring cells on this cell. If he is unable to do that, game ends. Determine the smallest number of stones he has to place in the beginning so he has a strategy to make the game last for at least 20232023 rounds.
combinatorics