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Doodles

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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

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Fitting In

Age 14 to 16 Challenge Level:

The largest square which fits into a circle is $ABCD$ and $EFGH$ is a square with $E$ and $F$ on the line $AB$ and $G$ and $H$ on the circumference of the circle. Show that $AB = 5EF$.

circle with squares ABCD and EFGH inside it.

Similarly the largest equilateral triangle which fits into a circle is $LMN$ and $PQR$ is an equilateral triangle with $P$ and $Q$ on the line $LM$ and $R$ on the circumference of the circle. Show that $LM = 3PQ$.

circle with squares LMN and PQR inside it.