## Subtract a square |

**Subtract-a-square** (also referred to as **take-a-square**) is a two-player mathematical game of strategy. It is played by two people with a pile of coins (or other tokens) between them. The players take turns removing coins from the pile, always removing a non-zero * normal play* game, which means that the player who removes the last coin wins.

A normal play game starting with 13 coins is a win for the first player provided (s)he starts with a subtraction of 1:

player 1: 13 - 1*1 = 12

Player 2 now has three choices: subtract 1, 4 or 9. In each of these cases, player 1 can ensure that within a few moves the number 2 gets passed on to player 2:

player 2: 12 - 1*1 = 11 player 2: 12 - 2*2 = 8 player 2: 12 - 3*3 = 3 player 1: 11 - 3*3 = 2 player 1: 8 - 1*1 = 7 player 1: 3 - 1*1 = 2 player 2: 7 - 1*1 = 6 or: 7 - 2*2 = 3 player 1: 6 - 2*2 = 2 3 - 1*1 = 2

Now player 2 has to subtract 1, and player 1 subsequently does the same:

player 2: 2 - 1*1 = 1 player 1: 1 - 1*1 = 0 player 2 loses