Answer to Question #27713 in Combinatorics | Number Theory for aishwarya

Question

Pam and sipho are playing cards. They take it in turns to remove one, two or three cards from the pack, they may remove the same number of cards as the previous player. For example, if pam removes three cards then sipho can only remove one or three cards and so on. The winner of the game is the person who takes either the last card, or leaves the other player with no valid moves. For the investigation suppose that pam always starts first and both pam and sipho play to win. Answer the following questions: (a) investigate who would win if the pack of cards has as many as 13 cards in it. (B) who would win with a pack of 15cards? Explain fully. (C) who would win with a pack of 16cards? (D) who would win if sipho and pam play with a full pack of 52, or even 99 cards?