Monday, February 20, 2017

Block Pyramids

The drawings below show a 1-layer, 2-layer, and 3-layer pyramid made out of color cubes.  There is one visible block on the first one, 5 on the second one, and 13 on the third one.  "Visible blocks" are those that you can see if you were to walk around the pyramid.
How many blocks would be visible on a 6-layer pyramid? 35-layer pyramid? n-layer pyramid?
How many square units of paint would be used (total faces painted) in an n-layer pyramid?

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