Now 我同意第二步 and I add my 第3步 to reach 99.1%

Background: 第二步

the key of your 2nd step is actually because 2^n - 2^m 10 ^n (n>=2)!. in plain language: you can never mess 1 hat but get the same last 2 digits.

Now remember it actually also right 2^n - 2^m 1 . you can never mess up 1 hat but get the same last 1 digit!.

So, 第3步 ~~~

- you only need to know the last ONE digit and 會發現隻有 ONE arrangement可以由匯總得到的2進製數通過轉換１位數字得到... 99.1% now!



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Now 第4步

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note: let's say n= # of colors...
now if going through the long way and hard way (馬後炮 though), we do not need to trap ito the 2進製 n進製 and you can eliminated the 進製transitions and exclusions.... Use n 進製 directly - that's the final simple and sweet answer posted earlier!

:)

所有跟帖： 

• 嗬嗬，我不同意第三步。 -wxczcbm- ♂ (470 bytes) () 02/19/2010 postreply 21:18:23

• Yeah, u r Right. .... 10^1 is actually =10 not 1 -guest007- ♀ (53 bytes) () 02/20/2010 postreply 06:38:29