Another game of nim (Posted on 2004-09-02)

	Submitted by Brian Smith
Rating: 3.0000 (2 votes)
Solution:	(Hide)
The strategy for this game of nim is based off mod 8. If the number of tokens remaining is 0 or 2 mod 8, then the player is in a losing position. If the number of tokens remaining is 1 mod 8, then the only winning move is to take 1 token. If the number of tokens remaining is 3 mod 8, then the possible winning moves are to take 1 or 3 tokens. If the number of tokens remaining is 4 or 6 mod 8, then the only winning move is to take 4 token. If the number of tokens remaining is 5 mod 8, then the possible winning moves are to take 3 or 5 tokens. If the number of tokens remaining is 7 mod 8, then the only winning move is to take 5 tokens. In the case of 30 tokens in the problem: Since 30 mod 8 = 6, The first player can win by taking 4 tokens. Nikki expands the problem by finding a strategy for all variations of nim which remove any one option from a set of consecutive values starting at 1 (for this problem, 2 was removed from the set 1-5) here and here

	Subject	Author	Date
	Puzzle Thoughts	K Sengupta	2023-05-13 01:13:39
	re(4): Solution - Generalized!	Bruce Brantley	2004-09-08 10:55:38
	re(4): Solution - Generalized!	Brian Smith	2004-09-03 22:50:33
	re(3): Solution - Generalized!	nikki	2004-09-03 10:42:58
	re(2): Solution - generalized?	nikki	2004-09-03 08:32:43
	re: Solution - Embarrassed?	Bruce Brantley	2004-09-03 00:18:53
	Analysis	Federico Kereki	2004-09-02 19:34:22
	Solution - with explanation/thought process	nikki	2004-09-02 16:29:30
	re: Solution	Rajal	2004-09-02 16:16:16
	the strategy	Charlie	2004-09-02 16:11:40
	Solution	Rajal	2004-09-02 16:07:48