Problem:
The faces of two identical regular tetrahedra are colored red, white, green, blue; the colors are chosen randomly, but the four faces of each tetrahedron must all be of different colors. What is the probability that after the coloring the two tetrahedra are indistinguishable?
Pick one
Solution
Solution:
The answer is (D). Let us rest both tetrahedra on the red face and rotate them until the white face is in front of us. At this point there are two possible cases, the one on the right can be green or blue. Whatever color that of the first tetrahedron is, the probability that in the second it is of the same color and that therefore the two tetrahedra are indistinguishable is .
Want a route through all this instead of an archive? The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.