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Please note: Although it involves only elementary mathematical ideas, this problem is very difficult and will probably take a long time to solve!  

A mathematician goes into a supermarket and buys four items.

It has been a while since she has used a calculator and she multiplies the cost (in pounds, using the decimal point for the pence) instead of adding them.

At the checkout she says, "So that's £7.11" and the checkout man, correctly adding the items, agrees.

Find four possible prices of the items.

Extension: Prove that the costs giving rise to £7.11 are unique.
This problem is adapted from "Sums for Smart Kids" by Laurie Buxton, published by BEAM Education