jrrt@hogpd.UUCP (R.MITCHELL) (07/27/84)
The following puzzle was brought to my attention by Chris Sotinsky.
I don't know where she got it. I solved it using a fairly complex
combinatorial approach; Chris says she used a different solution
method, and her initial source had a third procedure. So now I'm
curious: how many different ways are there to solve it? I'd be
interested if people would *mail* me solutions. After a week or so,
when responses run dry, I'll post summaries of the different
approaches people used.
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Each of the four faces of a regular tetrahedron is divided into four
congruent equilateral triangles, vaguely approximated by the below diagram:
/\
/ \
.----.
/ \ / \
/ \/ \
----------
You are given four colors with which to paint the solid: red, Green,
Blue, and yellow. You must paint the solid in accordance with the
following rules:
1) Only two colors are to be used on each of the four faces.
2) Four small triangles are to be painted with each of the four
colors.
3) No two triangles having one side in common are to be painted the
same color.
Two "paintings" are said to be 'the same' if any rotation of one painting
in three-dimensional space duplicates the color scheme of the second.
How many different ways are there to color the tetrahedron?
Rob Mitchell
{allegra,ihnp4}!hogpd!jrrt