Q: How many different ways can you

paint a tetrahedron using no more than 4

colors?

A: 36

Unfold a tetrahedron so you get four triangles in the fashion of a first iteration Sierpinski triangle.

/\
/ \
/ \ 1234 1234 1234 1234
/ \ BBBB BBBG BBBR BBBY
/ 1 \ BBGG BBGR BBGY BBRR
/ \ BBRY BBYY BGGG BGGR
/____________\ BGGY BGRR BGRY BGYR
/\ /\ BGYY BRRR BRRY BRYY
/ \ / \ BYYY GGGG GGGR GGGY
/ \ 2 / \ GGRR GGRY GGYY GRRR
/ \ / \ GRRY GRYY GYYY RRRR
/ 3 \ / 4 \ RRRY RRYY RYYY YYYY
/ \ / \
/____________\/____________\