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?
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?
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?
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.