imc

Question

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?

Accepted Answer

We write out the 5!=120 cases, then filter out the valid ones: 13254,14253,14352,15243,15342,21435,21534,23154,24153,24351,25143,25341, 31425,31524,32415,32514,34152,34251,35142,35241,41325,41523,42315,42513, 43512,45132,45231,51324,51423,52314,52413,53412. We count these out and get 32 permutations that work.