也出一個game

An array of stones (N x M), two players taking turns removing stones.

When a stone is selected, the stones lie above and right are also removed.

The loser is the one ends up removing the last stone.

For instance, for 3x5 number of stones:

a b c d e

f g h i j

k l m n o

 

If a player selects the i stone,  d, e, i, j are all removed.

Does this game have a first mover advantage? What's your strategy?

 

 

 

 

所有跟帖： 

• Red Grit, let us try your game. -jinjing- ♀ (108 bytes) () 05/26/2011 postreply 05:36:13

• u r right, but I need a more general strategy... -丹砂- ♀ (340 bytes) () 05/26/2011 postreply 13:44:27

• 網上犯了邏輯錯誤,後手策略是隨先手變的..... -jinjing- ♀ (168 bytes) () 05/26/2011 postreply 16:24:08

• 不覺得證明有錯，因為取了(i,j)，和先取(M,N)後取(i,j)結果一樣 -丹砂- ♀ (95 bytes) () 05/26/2011 postreply 18:14:00

• 3X4時，先拿右上角那一個，敗勢 -15少- ♂ (0 bytes) () 05/27/2011 postreply 02:31:53

• 不會吧。。。 -丹砂- ♀ (106 bytes) () 05/27/2011 postreply 06:24:13

• 回複：不會吧。。。 -15少- ♂ (687 bytes) () 05/27/2011 postreply 07:11:04

• oh, 剛才沒想清楚。看來策略跟奇偶有關。。。 -丹砂- ♀ (0 bytes) () 05/27/2011 postreply 07:37:31

• 隻拿一個是讓先，必輸 -15少- ♂ (0 bytes) () 05/27/2011 postreply 09:17:27

• Your right, I'm too busy to care in the end of semest.er. -jinjing- ♀ (38 bytes) () 05/29/2011 postreply 09:10:20

• The top right one is a bad move, except for 2x2 -15少- ♂ (36 bytes) () 05/27/2011 postreply 09:15:53

• 2x3呢？再往下推導就是2xn都可以top right one -丹砂- ♀ (0 bytes) () 05/27/2011 postreply 09:32:36

• ops, except for 2xN -15少- ♂ (0 bytes) () 05/27/2011 postreply 09:37:47

• For any finite matrix, the first player wins -Pantsonfire- ♀ (371 bytes) () 05/26/2011 postreply 19:02:20

• thx a lot for the info -丹砂- ♀ (0 bytes) () 05/27/2011 postreply 06:24:42