pam and sipho are playing cards. they take it in turns to remove one, two or three cards from the pack, but they may never remove the same number of cards as the previous player. if for example pam removes two cards then sipho can only remove 1 or 3 cards etc. the winner of the game is the person who takes either the last card or leaves the other player with no valid moves. suppose pam always goes first, investigate who would win if the pack has 13 cards. then if the pack has 15 cards who would win with 16 cards? finally who would win with a full pack of 99 cards?