You need to make a set of five rods for a magic trick, with numbers on them ranging from 1 to 31 inclusive. Then you ask people to pick a number and show you

**only the top number** of whatever rods it is on. From that you have to guess which number the person picked. This has to be done within a few seconds and isn't a matter of remembering what numbers are on them.

What numbers should be on each of the five rods?

__Rod 1__
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31

__Rod 2__
2, 3, 6, 7, 10, 11, 14, 15, 18,19, 22, 23, 26,27, 30, 31

__Rod 3__
4, 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 23, 28, 29, 30, 31

__Rod 4__
8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31

__Rod 5__
16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31

The top numbers should be the FIRST one in each list...

The first number is 2^(x-1) (where x is the number of the rod), and all the numbers on each rod contain that first numbered bit when expressed in base 2 (binary).

*Edited on ***November 11, 2003, 1:44 pm**