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?

所有跟帖： 

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

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

• 回复：A game -letmeregister- ♂ (419 bytes) () 05/20/2011 postreply 07:28:14

• 回复：回复：A game -jinjing- ♀ (965 bytes) () 05/20/2011 postreply 17:18:18

• This answer can fit any arrangement of this game -北京大老猫- ♀ (141 bytes) () 05/22/2011 postreply 12:37:25

• 回复：This answer can fit any arrangement of this game -jinjing- ♀ (140 bytes) () 05/23/2011 postreply 05:50:04

• 谢谢掺和~~~ -北京大老猫- ♀ (0 bytes) () 05/22/2011 postreply 12:38:14

• 这类题叫NIM -丹砂- ♀ (39 bytes) () 05/24/2011 postreply 17:42:26

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

• 回复：1st loses: 2nd player Keeps odd number of rows and odd number -jinjing- ♀ (117 bytes) () 05/26/2011 postreply 05:55:04