MathDB

Three players

A,B

and

C

take turns removing stones from a pile of

N

stones. They move in the order

A,B,C,A,B,C,…A

. The game begins, and the one who takes out the last stone loses the game. The players

A

and

C

team up against

B

, they agree on a joint strategy.

B

can take in each play

1,2,3,4

5

stones, while

A

and

C

, they can each get

1,2

3

stones each turn. Determine for what values of

N

have winning strategy

A

and

C

, and for what values the winning strategy is from

B

. .

Problem Statement