There are 100 pebbles on the table. There are two players, A and B, who move alternatively. Player A moves first. The rules of the game are the same for both players: at each move they can remove one, two, three, four of five pebbles. The winner is the player who takes the last pebble. Who is guaranteed to win provided that he plays properly? Convince me why you think this. Same question if the one who takes the last pebble loses.