How many arrangements of the numbers 1, 2, 3, ..., 7, 8, 9 are there where the sum of any two adjacent numbers is odd?
It seems like swapping the even numbers around with eachother would do the trick. In this series there are 4 even numbers, they can be rearranged in 4! ways or 4x3x2x1 = 24.
See this link: https://web2.0calc.com/questions/counting_92640