Difference between revisions of "2021 AMC 10A Problems/Problem 20"
Line 4: | Line 4: | ||
==Solution (bashing)== | ==Solution (bashing)== | ||
− | We write out the 120 cases. | + | We write out the <math>120</math> cases. |
These cases are the ones that work: | These cases are the ones that work: | ||
− | <math>1,3,2,5,4</math> | + | <math>1,3,2,5,4 \linebreak</math> |
− | <math>1,4,2,5,3</math> | + | <math>1,4,2,5,3 \linebreak</math> |
− | <math>1,4,3,5,2</math> | + | <math>1,4,3,5,2 \linebreak</math> |
− | <math>1,5,2,4,3</math> | + | <math>1,5,2,4,3 \linebreak</math> |
− | <math>1,5,3,4,2</math> | + | <math>1,5,3,4,2 \linebreak</math> |
− | <math>2,1,4,3,5</math> | + | <math>2,1,4,3,5 \linebreak</math> |
− | <math>2,1,5,3,4</math> | + | <math>2,1,5,3,4 \linebreak</math> |
− | <math>2,3,1,5,4</math> | + | <math>2,3,1,5,4 \linebreak</math> |
− | <math>2,4,1,5,3</math> | + | <math>2,4,1,5,3 \linebreak</math> |
− | <math>2,4,3,5,1</math> | + | <math>2,4,3,5,1</math> |
<math>2,5,1,4,3</math> | <math>2,5,1,4,3</math> | ||
<math>2,5,3,4,1</math> | <math>2,5,3,4,1</math> |
Revision as of 15:22, 11 February 2021
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: We count these out and get permutations that work. ~contactbibliophile