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Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

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Russian Cubes

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?

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N000ughty Thoughts

How many noughts are at the end of these giant numbers?

Counting Binary Ops

Age 14 to 16 Challenge Level:
The underlying structure of this problem is very similar to Walkabout. The teachers' notes to Walkabout suggest a possible approach which would work here too.