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'Shopping Basket' printed from http://nrich.maths.org/
Please note: Although it involves
only elementary mathematical ideas, this problem is very difficult
and will probably take a long time to
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.
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