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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

Age 14 to 16 Challenge Level:

This problem offers an opportunity:
  • to notice and explain patterns in a multiplication square
  • to use some algebraic techniques, in particular multiplying out brackets.