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Doodles

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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Picture Story

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

Multiplication Square

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

For a general $2$ by $2$ square, the column headings could be $x$ and $(x + 1)$, and the row headings could be $y$ and $(y + 1)$.

For a general $3$ by $3$ square, the column headings could be $x$, $(x + 1)$ and $(x + 2)$, and the row headings could be $y$, $(y + 1)$ and $(y + 2)$.

If you are struggling with the algebra take a look at Partitioning revisited.