Question 13
There are three piles of tokens on the table: the first contains $a$, the second $b$ and the third one $c$ tokens, and $a \ge b \ge c \gt 0$. Two players $A$ and $B$ take turns moving the tokens around. Player $A$ goes first. For each move, the active player first chooses two piles and then moves at least one token from the pile with fewer tokens into the pile containing more tokens. If the numbers of tokens in the two chosen piles are equal, then the player moves at least one token from any of them onto the other. A player wins if there is only one pile remaining after their move. Who has the winning strategy for different values of $a, b$ and $c$?