It is always good to hear how, when provide with a simple starting point, children can take mathematics beyond our expectations. Here is an account of such an event from a teacher.....

"Our school, Barford St Peters Primary in Warwickshire, has an after-school Maths Club for juniors where we often look at nrich problems. I explained this problem to them, and most of them decided to work on it from a slightly different angle; they looked at the different possible total amount, from 1p up to 100p, and worked out if this was possible with 5 coins, and if so, which 5 coins would do it. Dean, Liam and Andrew worked up to about 40 in the time available, and decided that only 1p,2p, 3p and 4p were impossible with 5 coins.

Then, in his own time, Andrew (aged 7) decided that he wanted to consider, for a given number of coins, what was the smallest total which required that number of coins. His first answer was that 38p was the smallest amount which required 5 coins, 88p the smallest to need 6 coins. He worked out that £5.88 was the smallest to need 9 coins (£2, £2,£1,50p, 20p 10p 5p2p1p), but that £7.88 needed 10 coins (Another £2 plus the ones before). He reckoned £17.88 needed 15 coins, £27.88 needed 20 coins, £37.88 needed 25 coins, £187.88 needed 100 coins, and then went off into the realms of trillions of coins and googols of coins!"