This is a very tricky problem and it has puzzled many of you for several months. However, Douglas at Burgoyne Middle School has cracked it. He says that he found a similar problem in a book which actually gave three of the prices. This made it a bit easier to get started.

Douglas lists the answers as:
£1.20, £1.25, £1.50 and £3.16.

Unfortunately, when we asked how he did it, Douglas couldn't remember his method.
If you think that you can explain how to arrive at these prices, please let us know.