Proof of 4. It is fun.

来源: wxcfan123 于 2011-08-03 08:27:10 [] [旧帖] [给我悄悄话] 本文已被阅读： 0 次 (649 bytes)
回答: 1) 1,5,7,11. 4) (2n-1)!! 由 康MM 于 2011-08-02 16:02:20

Let S(n) be required.\

1. The weight start with 2^0 or 2^1 have the same S(n).

2. The first weight should be placed on left - first weight rule.

3. S(n) = 1.

4. n+1. Consider weight 1 (not 2^n that make thing compicated, and could scare people like me). It can be insert at any time and either side except the first weight rule. So, have 2n+1. The rests have S(n). Note that even weight 1 is added at the first time on left, it does not break the first weight rule of the rest n.

So, we have S(n+1) = (2n+1)S(n). Done.

Without knowing the result, I do not think I could solve it.

 

所有跟帖： 

• let me show U, fn=(n+1)!/2. I'm right,MM is... -jinjing- ♀ 给 jinjing 发送悄悄话 (469 bytes) () 08/03/2011 postreply 12:48:41

• Jingling, your answer is obviously wrong. Wxc's proof is beautif -乱弹- ♂ 给 乱弹 发送悄悄话 乱弹 的博客首页 (238 bytes) () 08/04/2011 postreply 10:06:43

• How are you,Ｍy answer is right is right,though my right side is -jinjing- ♀ 给 jinjing 发送悄悄话 (173 bytes) () 08/04/2011 postreply 13:32:34

• my right side is Q's left side, -jinjing- ♀ 给 jinjing 发送悄悄话 (0 bytes) () 08/04/2011 postreply 13:35:51

• 唉，怎么说呢。N=3，见内。 -wxcfan123- ♂ 给 wxcfan123 发送悄悄话 (295 bytes) () 08/04/2011 postreply 14:09:00

• Thx,your right,I am sorry ,My answer is for last states.not求整个操作 -jinjing- ♀ 给 jinjing 发送悄悄话 (29 bytes) () 08/04/2011 postreply 14:30:48

• My solution, it is not Dct. -jinjing- ♀ 给 jinjing 发送悄悄话 (226 bytes) () 08/04/2011 postreply 18:07:45

• Your (n-1)! * 2^{n-1}is not right, should be n!, n=3,first is he -jinjing- ♀ 给 jinjing 发送悄悄话 (22 bytes) () 08/04/2011 postreply 14:11:09

• I am sorry ,My answer is for last states.not求整个操作过程的不同方法个数． -jinjing- ♀ 给 jinjing 发送悄悄话 (0 bytes) () 08/04/2011 postreply 14:27:34

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