Question 34
Two people, $A$ and $B$, play by removing coins from a pile that initially contains $2006$ coins. Players play in turns, removing $1$ to $7$ coins each turn; Each player keeps with him the coins he has removed. If a player wishes, he can pass (not remove coins on his turn) but to do so he must pay $7$ coins that he removed from the stack on previous turns. These $7$ coins are placed in a separate box and no longer play a role in the game. Whoever removes the last coin wins, and $A$ begins the game.
Determine which of the two players can ensure victory, no matter how the other plays. Show a winning strategy and explain why it is a winner.
Determine which of the two players can ensure victory, no matter how the other plays. Show a winning strategy and explain why it is a winner.