A game

Suppose that there are four rows of paper clips. The first row has one paper clip, the second row has 3, the third has 5, and the fourth has 7. Two players take alternating turns in which they take away some paper clips. During a turn, a player may take any number of paper clips from a row, but may only take paper clips from that row. For example, if the first player on the first turn decides to take from the third row, he can take 1, 2, 3, 4, or 5 paper clips from that row, but he cannot also take a paper clip from the second row. The player who takes the last paper clip loses.

Which player, the one who goes first or the one who goes second, wins? How can he guarantee a win?

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The first lost.this case is special,most other cases,the first w -jinjing- 給 jinjing 發送悄悄話 (130 bytes) () 05/15/2011 postreply 09:31:36

sorry,careless.I woildthink who take the last who win.In your Q, -jinjing- 給 jinjing 發送悄悄話 (26 bytes) () 05/15/2011 postreply 09:45:08

回複:A game -letmeregister- 給 letmeregister 發送悄悄話 (419 bytes) () 05/20/2011 postreply 07:28:14

回複:回複:A game -jinjing- 給 jinjing 發送悄悄話 (965 bytes) () 05/20/2011 postreply 17:18:18

This answer can fit any arrangement of this game -北京大老貓- 給 北京大老貓 發送悄悄話 北京大老貓 的博客首頁 (141 bytes) () 05/22/2011 postreply 12:37:25

回複:This answer can fit any arrangement of this game -jinjing- 給 jinjing 發送悄悄話 (140 bytes) () 05/23/2011 postreply 05:50:04

謝謝摻和~~~ -北京大老貓- 給 北京大老貓 發送悄悄話 北京大老貓 的博客首頁 (0 bytes) () 05/22/2011 postreply 12:38:14

這類題叫NIM -丹砂- 給 丹砂 發送悄悄話 丹砂 的博客首頁 (39 bytes) () 05/24/2011 postreply 17:42:26

1st loses: 2nd player Keeps odd number of rows and odd numbers o -修volvo- 給 修volvo 發送悄悄話 (33 bytes) () 05/24/2011 postreply 21:43:59

回複:1st loses: 2nd player Keeps odd number of rows and odd number -jinjing- 給 jinjing 發送悄悄話 (117 bytes) () 05/26/2011 postreply 05:55:04

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