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### Number and algebra

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# Coins

A man has 5 coins in his pocket.

Given these clues, can you work out what the coins are?

Is there only one possible combination of coins?

### Extension:

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Age 11 to 14

Challenge Level

A man has 5 coins in his pocket.

- He can make 13 different amounts of money with his coins

- The amounts of money he can make end with one of two possible digits.

- He cannot make up exactly 70 pence

- He cannot afford an item costing 1 pound

- He can make a prime number bigger than 10 with his coins.

Given these clues, can you work out what the coins are?

Is there only one possible combination of coins?

Remove one of the clues. Are there any new possibilities for the values of the 5 coins?

Replace that clue and remove a different one, work out the new possibilities. Repeat for the other clues.

Can you remove a clue and only end up with your original solution(s)?

Which clues have the biggest impact?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?