Existence Proofs II

Futility Closet has another example of an existence proof like their previous one taken from Peter Winkler’s 2021 Mathematical Puzzles (see my post “Existence Proofs”):

“Four bugs live on the four vertices of a regular tetrahedron. One day each bug decides to go for a little walk on the tetrahedron’s surface. After the walk, two of the bugs have returned to their homes, but the other two find that they have switched vertices. Prove that there was some moment when all four bugs lay on the same plane.”

See Existence Proofs II

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