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2000 SMT/Advanced Topics Problems/Problem 1

Revision as of 12:55, 22 July 2020 by Orca25 (talk | contribs) (Created page with "==Problem== How many different ways are there to paint the sides of a tetrahedron with exactly 4 colors? Each side gets its own color, and two colorings are the same if one c...")
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Problem

How many different ways are there to paint the sides of a tetrahedron with exactly 4 colors? Each side gets its own color, and two colorings are the same if one can be rotated to get the other.


SMT Solution

Assume we have 4 colors - 1, 2, 3, and 4. Fix the bottom as color 1. On the remaining sides you can have colors 2, 3, 4 (in that order), or 2, 4, 3, which are not rotationally identical. So, there are $\mathbf{2}$ ways to color it.




Credit

Problem and solution were taken from https://sumo.stanford.edu/old/smt/2000/

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