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A square patio was tiled with square tiles all the same size. Some of the tiles were removed from the middle of the patio in order to make a square flower bed, but the number of the remaining tiles was still a square number. What were the dimensions of the patio and the flower bed?

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Time of Birth

A woman was born in a year that was a square number, lived a square number of years and died in a year that was also a square number. When was she born?

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Small Change

In how many ways can a pound (value 100 pence) be changed into some combination of 1, 2, 5, 10, 20 and 50 pence coins?

Cola Can

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This printable worksheet may be useful: Cola Can.

Once the lower level thinking covered in the Hint has been assimilated students might be guided if necessary to see the value of a spreadsheet when solving a problem of this sort.

Additionally the use of a graph representing the spreadsheet values is particularly helpful for 'picturing' the behaviour of the surface area function as either base radius or can height varies.

There is a valuable opportunity to work with each of the two obvious independent variables : base radius and height. Starting with either of these the other is calculable from the specified volume of 330 ml, and once both r and h are known the surface area is calculable.