# Puzzles

## The taxman

Source: New York Times

In a very strange country, the tax system works as follows.

£1, £2, £3 up to £12 are available.

You pick an amount. You keep this amount, but the taxman takes any factors of it. You cannot pick any amount without a factor.

This continues until you can take no more money. The taxman gets any remaining money.

For example, you might play as follows:

- Take £12. Taxman gets £1, £2, £3, £4, £6.
- Take £10. Taxman gets £5.
- You cannot take anything. Taxman gets £7, £8, £9, £11.

In this example, you end with £22 and the taxman ends with
£56.

Is it possible to get more money than the taxman? What is the most you can get?

If you enjoyed this puzzle, check out Sunday Afternoon Maths XLII,

puzzles about numbers, or a random puzzle.

puzzles about numbers, or a random puzzle.