KöMaL 2006 B3926

Ann and Bob are playing the following game: There are 10 heaps of pebbles in front of them. The first heap contains 1 pebble, the second one contains 2, the third one contains 3, and so on, the tenth heap contains 10 pebbles. They take turns in carrying out one of the following two moves: they either divide a heap into two smaller ones or remove one pebble from one heap. A player who cannot do so any more will lose the game. Determine which player has a winning strategy, given that Ann starts the game.