Question 37
There are three piles of tokens on a table, containing $a,b,c$ tokens, where $a\ge b\ge c\gt0$. Players $A$ and $B$ move tokens alternately, with $A$ starting. On each move a player chooses two piles and transfers at least one token from the smaller pile to the larger one. If the chosen piles are equal, tokens may be moved from either pile to the other. The player whose move puts all tokens in a single pile wins. Determine who has a winning strategy, depending on $a,b,c$.