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The number of hidden cubes 2002-02-05
From Katie:
This problem is about finding the number of cubes visible and hidden in a cube.

In a cube that is 3x3, 19 cubes can be seen. 8 are hidden.
In a cube that is 4x4, 37 cubes can be seen. 27 are hidden.
In a cube that is 5x5, 61 cubes can be seen. 64 are hidden.
In a cube that is 6x6, 91 cubes can be seen. 125 are hidden.

The question is:
Explain how you could find the number of small cubes that are visible and hidden in a cube of any size.

Answered by Paul Betts and Penny Nom.



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