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## 'Cogs' printed from http://nrich.maths.org/

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A and B are two interlocking cogwheels having p teeth and q
teeth respectively where $$3\leq q\leq p \leq
12$$

One tooth on B is painted red. Find the values of p and q for
which this red tooth on B contacts every gap on the cogwheel A as
the wheels rotate.