Problem of the Day #426: Honey DropsJanuary 2, 2013

Posted by Saketh in : potd , trackback

Two bears are sharing some honey they found by playing a little game. They get two pots, and divide the honey (not necessarily evenly) between the pots. Let the first pot contain $a$ drops of honey, and let the second contain $b$ drops of honey.

The game proceeds as follows. Each turn, one of the bears takes $2k$ drops of honey from one of the pots, eats $k$ of the drops, and places the other $k$ drops in the other pot. The bears alternate until no valid move is available, at which point the last bear to move wins.

For which values of $a$ and $b$ does the bear that goes first have a winning strategy?