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

Express the numbers in binary:

1111=15
0111=7
1011=11
0011=3
1101=13
0101=5
1001=9
0001=1
1110=14
0110=6
1010=10
0010=2
1100=12
0100=4
1000=8
0000=0

The first bit switches every number, the second bit switches after 2 numbers, the third after 4 numbers, and the fourth after 8 numbers.

Another simpler solution (which is probably the one Jer intended) is it's the numbers 15 to 1 in binary, except each number is written backwards (ie instead of 1111, 1110, 1101, 1100... it's 1111, 0111, 1011, 0011... )

The sequence could be written with 0 or not, since it comes at the end.

Posted by Gamer on 2006-12-29 17:55:47