### Brain Teasers

# Magic Rods

You need to make a set of five rods for a magic trick, with numbers on them ranging from 1 to 31 inclusive (although each rod does not contain all of the numbers). 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 six rods?

What numbers should be on each of the six rods?

### Hint

Think of a system used in computers.### Answer

The numbers should be: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

This uses the same idea as the binary system. All you do is add up the first numbers of the rods that have the number on. It works because the first numbers of each rod are 1,2,4,8 & 16, and using those numbers you can make any numbers from 1 to 31. For example, to make 25 you use the numbers 1,8 and 16, which are rods 1,4 and 5, so 25 is only written on those three rods.

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