[中译] Puzzleup 2014 (12) Binary Digits

楼主: LPH66 (-6.2598534e+18f)   2014-10-22 22:05:20
题目网址: http://www.puzzleup.com/2014/
http://www.puzzleup.com/2014/puzzle/?253
答题时限: 10月16日7PM-比赛结束(约12月17日)
加分时限: 10月16日7PM-10月22日6:59PM
答对可得基本分100分。答案可上传5次,每改1次答案从基本分扣20分。 
比赛期间内可随时上传答案,加分时限内答对第n天加(6-n)分       
另依题目的难易有额外加分(如有80%的人这题答错,答对者加80分)  
◆Binary Digits
Insert 5 commas between the digits of 21218453415461109221 and obtain 6
numbers, so that no two consecutive digits will be the same in the binary
representation of these numbers.
What is the sum of these 6 numbers?
If the problem was asked for 542 with one comma, then the answer would be 47
(5+42=47).
The binary representation of 5 is 101, the binary representation of 42 is
101010, and no two consecutive digits are the same in these numbers.
在数字 21218453415461109221 当中插入 5 个逗号形成 6 个数字,
使得在这些数字的二进制表示法中没有任何两个相邻数位是相同的。
这 6 个数字的和是多少?
若题目改问 542 及 1 个逗号, 则答案为 47 (5+42=47):
5 的二进制为 101,42 的二进制为 101010,它们都没有两个相邻数位相同。

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