How many arrangements of the numbers 1, 2, 3, ..., 7, 8, 9 are there where the sum of any two adjacent numbers is odd?

1, 2, 3, 4, 5, 6, 7, 8, 9 O==Odd, E==Even

O, E, O, E, O, E, O, E, O

There are 5 odd numbers ==5!

There are 4 even numbers =4!

Total number of arrangements ==5! x 4! ==2,880