Stage: 4 Challenge Level: 
Why do this problem?
This is a short problem that can be used as a lesson starter and it is non-standard so the learners have to think how to apply what they know. The problem also requires the learner to work systematically to be sure they have considered all possible cases and found all the solutions.
Possible approach
Let the class work on the problem and then make a list of all the solutions that they have found.
Key Questions
Have we found all possible solutions?
How can we be sure?
Inequality/inequalities. Number theory. Stage 5 - Reviewed 2012. Algebra - generally. Generalising. Golden ratio. Quadratic equations. Manipulating algebraic expressions/formulae. Mathematical reasoning & proof. Index notation/Indices.
Published October 2003.
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