How do i get n alternating patern split into two groups

Question

If i have 120 alternating boy and girls in a single file line, and i have to have neighboring partners switch so that all the boys are on one side and all the girls are on the other side, how many minimum switches would i have to make?

Answer 1

Always helpful to try to find the pattern with a smaller number, say 3 pairs.

 

X O X O X O

X X O X O O

X X X O O O

 

3 Switches

 

Test with another number

 

X O X O X O X O X O

X X O X O X O X O O

X X X O X O X O O O 

X X X X O X O O O O

X X X X X O O O O O

 

So 60 pairs, 60 switches.