Usenet Newsgroups : rec.puzzles Hall of FameThe rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided. Many of these puzzles also appear in Braingle's own collection. 

0 01 01011 0101101011011 0101101011011010110101101101011011 etc. Each string is formed from the previous string by substituting '01' for '0' and '011' for '1' simultaneously at each occurance. Notice that each string is an initial substring of the previous string so that we may consider them all as initial substrings of an infinite string. The puzzle then is, given n, determine if the nth digit is 0 or 1 without having to construct all the previous digits. That is, give a nonrecursive formula for the nth digit.
Solution