Question 184
Alice and Ben play the game on a board with $72$ cells around a circle. First, Ben chooses some cells and places one chip on each of them. Each round, Alice first chooses one empty cell and then Ben moves a chip from one of the adjacent cells onto the chosen one. If Ben fails to do so, the game ends; otherwise, another round follows. Determine the smallest number of chips for which Ben can guarantee that the game will last for at least $2023$ rounds.
(Václav Blažej)
(Václav Blažej)