Problem of the Day #74

POTD February 20, 2024

Alvin and Balvin are playing a game. In a pile are 2024 stones, Alvin and Balvin take turns removing stones from the pile. The only rule is that Alvin and Balvin must always remove a palindromic nonzero number of stones (e.g. Alvin can remove 101 stones from the pile making it have 1923 stones remaining). A player wins when on their turn, they remove all remaining stones. Alvin goes first, and Balvin goes second. If given that Alvin has a winning strategy, of all the possible number of stones that Alvin can take on his first turn that ensures a winning strategy, what is the minimum value of all these possible values of numbers of stones.