2021 AMC 10A Problems/Problem 20

Problem

In how many ways can the sequence $1,2,3,4,5$ be rearranged so that no three consecutive terms are increasing and no three consecutive terms are decreasing? $\textbf{(A)} ~10\qquad\textbf{(B)} ~18\qquad\textbf{(C)} ~24 \qquad\textbf{(D)} ~32 \qquad\textbf{(E)} ~44$

Solution (bashing)

We write out the $120$ cases. These cases are the ones that work: $13254, 14253, 14352, 15243, 15342, 21435, 21534, 23154, 24153, 24351, 25143, 25341, 31425, 31524, 32415, 32451, 34152, 34251, 35142, 35241, 41325, 41523, 42315, 42513, 43512, 45132, 45231, 51324, 51423, 52314, 52413, 53412,$ We count these out and get $\boxed{\text{D: }32}$ permutations that work. ~contactbibliophile

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2021 AMC 10A Problems/Problem 20

Problem

Solution (bashing)