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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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A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

One Basket or Group Photo

Stage: 2, 3, 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
As suggested in the question it helps to start with simple cases.