[中譯] Puzzleup 2014 (12) Binary Digits

作者: LPH66 (-6.2598534e+18f)   2014-10-22 22:05:20
題目網址: http://www.puzzleup.com/2014/
http://www.puzzleup.com/2014/puzzle/?253
答題時限: 10月16日7PM-比賽結束(約12月17日)
加分時限: 10月16日7PM-10月22日6:59PM
答對可得基本分100分。答案可上傳5次,每改1次答案從基本分扣20分。 
比賽期間內可隨時上傳答案,加分時限內答對第n天加(6-n)分       
另依題目的難易有額外加分(如有80%的人這題答錯,答對者加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.
在數字 21218453415461109221 當中插入 5 個逗號形成 6 個數字,
使得在這些數字的二進位表示法中沒有任何兩個相鄰數位是相同的。
這 6 個數字的和是多少?
若題目改問 542 及 1 個逗號, 則答案為 47 (5+42=47):
5 的二進位為 101,42 的二進位為 101010,它們都沒有兩個相鄰數位相同。

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