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'The Root Cause' printed from http://nrich.maths.org/

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Why do this problem?
It is instructive as an example of proof using the contrapositive of the statement that must be proved.

Possible approach
The class might discuss the proof in pairs before having a class discussion of the proof. It is very short but needs to be carefully argued.

Key question
What if the statement we are trying to prove were not true?

Possible support
Proof Sorter