The numbers 1 through 15 have been re-ordered according to a certain logic. Deduce the logic and fill in the blanks.

15, 7, 11, 3, ___, ___, ___, 1, 14, 6, ___, ___, 12, 4, 8

15,7,11,3,13,5,9,1,14,6,10,2,12,4,8

I noticed that S(n+8)=S(n)-1.  That is enough to fill in the numbers.

I also noticed that assuming S(0)=15 and S(16)=0, S(n)+S(16-n)=15

I believe that these qualities : S(n+8)=S(n)-1, S(0)=15, S(n)+S(16-n)=15 are enough to fill in the entire sequence.  However, I am not convinced that I got the intended logic.

Posted by Joel on 2006-12-29 12:33:41