Please Solve

Question

Two players, A and B, takes turns in the following game. There is a pile of six matchsticks. At a turn, a player must take one or two sticks from the remaining pile. The player who takes the last stick wins. Player A makes the first move and each player always makes the best possible move. Who wins the game?

 

 

Thanks for all the help I am receiving.

 

Karen

Answer 1

Player B always wins

 

You want to be in the position where it is the other players turn and there are 3 matches left

 

You can't lose becasue if the player takes one you take two and win, if the player takes two you take 1 and win.

 

In this case if Player A goes first and takes 1 then player B takes 2 and now it is player A turn with 3 left

 

If player A goes first and takes 2 then player B takes 1 and now it is player A turn with 3 left

 

No matter what Player A does at this point player B wins.