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Painted Tetrahedra (Posted on 2011-08-22) Difficulty: 3 of 5
You have an unlimited supply of wooden regular tetrahedra and N cans of paint, each of a different color.

You want to paint as many tetrahedra as possible given that you're limited to these N colors, with one color per face, but not requiring different colors on different faces, so that no two tetrahedra are identical. Two tetrahedra can count as non-identical even if they are mirror images, reversed.

It turns out that, given this value of N, you can make exactly as many tetrahedra with three colors as you can with four colors.

What's the value of N, the number of different colors available?

How many different tetrahedra do you have all together?

See The Solution Submitted by Charlie    
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re: I think .. (spoiler) | Comment 2 of 5 |
(In reply to I think .. (spoiler) by Steve Herman)

The intent was that the painter, wanting to make as many tetrahedra as possible, also made 1-color and 2-color tetrahedra in addition to the 3- and 4-color ones. It's just that the latter two matched in number, regardless of the 1- and 2-color ones also painted.
  Posted by Charlie on 2011-08-23 02:16:34

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