This is a chess play

Either first move or 2nd move wins. Since the player have the choice to select move, there a lot less play status that 2 player would win. These status can be enumberated.

To simplify the current question: An array of positive integers contains only member of 25. Each step, player can take one integer in the array minus it by 1 or 2 then break it into 2 integer if he want to. As possible to break (3) into (2), (1) and (1,1).

The player finish with array (1) wins the game.

It is not hard to know that following single element array (under 40) lead first player to lose:

(1), (4), (9), (12), (20)

25 is not one of them.

3 possible move for player 1 is (14, 10), (16, 8) and (18, 6)

所有跟帖： 

• 1,4,10,13,16,19,22,25......3M+1 FIRST LOST.I already proved. -jinjing- ♀ (172 bytes) () 03/21/2011 postreply 16:18:47

• You didn't thought enough. -letmeregister- ♂ (53 bytes) () 03/21/2011 postreply 16:43:03

• 回複：1,4,10,13,16,19,22,25......3M+1 FIRST LOST.I already proved. -letmeregister- ♂ (49 bytes) () 03/21/2011 postreply 16:45:31

• 回複：This is a chess play -fremontchin- ♀ (1771 bytes) () 09/02/2011 postreply 13:44:27