AMC 10 Step by Step
2024 AMC 10AProblem 6P1-10~2 minPrint

What is the minimum number of successive swaps of adjacent letters in the string ABCDEFABCDEF that are needed to change the string to FEDCBA?FEDCBA? (For example, 33 swaps are required to change ABCABC to CBA;CBA; one such sequence of swaps is ABCBACBCACBA.ABC\to BAC\to BCA\to CBA. )

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.