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Subtract a square
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Subtract a square : ウィキペディア英語版
Subtract a square

Subtract-a-square (also referred to as take-a-square) is a two-player mathematical game of strategy starting with a positive integer and both players taking turns subtracting a non-zero square number not larger than the current value. The game is usually played as a ''normal play'' game, which means that the last person who can make a subtraction wins.
== Illustration ==

A normal play game starting with the number 13 is a win for the first player provided he does start 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

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Subtract a square」の詳細全文を読む



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