Board Thread:Off-Topic Posts/@comment-32576568-20190405202604/@comment-36963837-20190510143054

bout 1,200,000 inches^2

Let n be a positive integer. Define a chameleon to be any sequence of 3n letters, with exactly n occurrences of each of the letters a, b, and c. Define a swap to be the transposition of two adjacent letters in a chameleon. Prove that for any chameleon X, there exists a chameleon Y such that X cannot be changed to Y using fewer than 3n²/2 swaps.