Question 10
C5 (SWE) At a round table are $1994$ girls, playing a game with a deck of $n$ cards. Initially, one girl holds all the cards. In each turn, if at least one girl holds at least two cards, one of these girls must pass a card to each of her two neighbors. The game ends when and only when each girl is holding at most one card.
(a) Prove that if $n\ge1994$, then the game cannot end.
(b) Prove that if $n\lt 1994$, then the game must end.
(a) Prove that if $n\ge1994$, then the game cannot end.
(b) Prove that if $n\lt 1994$, then the game must end.