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'Code to Zero' printed from http://nrich.maths.org/
Why do this problem?
To beat the spies at their own game!
It gives practice in working systematically to consider all cases.
First however you need to cut down the number of cases to be
checked, so think about the relation between $a$, $b$ and $c$ and
what you can deduce from it about the constraints on $a$, $b$ and
Ask the learners to find a relation between $a$, $b$ and $c$. Then
have a class discussion about what can be deduced from this
What do you know about $c^3-1$?