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

 Aug 29, 2021
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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

 Aug 29, 2021

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