I need help with this question. Im not too sure how to do it so an explanation would be helpful
Two people play the following game, starting with three piles of mathces. In a turn, a player moves any positive number of matches from one of the piles to a larger pile. The player who can’t make a move loses (the player who makes the last move wins). For example, in the position 17–12–12 you can move any number of matches from either of the piles of 12 to the pile of 17, but these are the only possible moves. In the position 9–6–3 you can move matches from the 3-pile to either of the other piles, and from the 6-pile to the 9-pile. Describe all final, losing and winning positions for this game (for any triple of numbers as pile sizes). Give a clear and concise argument for why your description is correct, that is, why these positions satisfy the conditions overleaf.