I have recently been struggling on a problem involving a modified game of Nim. I have tried finding an invariant or monovariant, but to no avail.
"In a game, Players X and Y take turns taking chips from a pile with P(at least 2) chips. Player X starts by taking at least one chip and at most P-1 chips. On each player's turn, they can take at least one chip but at most the amount the other player took on the previous turn. The player to take the last chip is the winner. What are all values of P such that Player Y has a winning strategy?"
Could anyone provide an answer with a rigorous proof? That would be very much appreciated!