Since submitting our last solution, the Y4 maths group have done some more investigation:
Money Bags – Part 2
When we looked again at the number of coins in each pot, we noticed that each number was double the previous one. Since double 8 is 16, we put 16 coins into the next empty pot so we had five pots containing 1p, 2p, 4p, 8p and 16p.
We knew the maximum price we could now pay would be 31p (our existing 15p plus the extra pot of 16p).
We checked that we could now make all of the prices from 15p to 31p (which we could – by adding the new pot of money to each of the combinations that we had already found). We knew that we had found a system and that the sixth pot should therefore contain 32p (which is double 16p) and that we would be able to make all of the prices up to a maximum of 63p.
We then came up with this sequence to show how much money twelve pots (two paint trays) would contain:
1p, 2p, 4p, 8p, 16p, 32p, 64p, £1.28, £2.56, £5.12, £10.24 £20.48