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?

With 5 rods you can represent 0 - 31 different numbers. Break each number down in to it's binary equivalent and on those rods write down the number. At the top of each rod, write the number 1 - 5 representing the least to most significant bits.

For example, take the number 19. In binary

10011

So, 19 would be written on the first, second and fifth rod.