2021 AMC 10A Problems/Problem 20
Revision as of 15:25, 11 February 2021 by Contactbibliophile (talk | contribs)
Problem
In how many ways can the sequence 
be rearranged so that no three consecutive terms are increasing and no three consecutive terms are decreasing?
Solution (bashing)
We write out the 
cases.
These cases are the ones that work:
\begin{align}
1,3,2,5,4
1,4,2,5,3
1,4,3,5,2
1,5,2,4,3
1,5,3,4,2
2,1,4,3,5
2,1,5,3,4
2,3,1,5,4
2,4,1,5,3
2,4,3,5,1
2,5,1,4,3
2,5,3,4,1
3,1,4,2,5
3,1,5,2,4
3,2,4,1,5
3,2,5,1,4
3,4,1,5,2
3,4,2,5,1
3,5,1,4,2
3,5,2,4,1
4,1,3,2,5
4,1,5,2,3
4,2,3,1,5
4,2,5,1,3
4,3,5,1,2
4,5,1,3,2
4,5,2,3,1
5,1,3,2,4
5,1,4,2,3
5,2,3,1,4
5,2,4,1,3
5,3,4,1,2
\end{align}
We count these out and get 
permutations that work. ~contactbibliophile
