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

 Mar 3, 2021
 #1
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for this, we would have to swap between odd and even numbers for the arrangement, so

4x3x3x2x2+4x3x3x2x2+4x3x3x2x2+4x3x3x2+4x3x3+4x3=$\boxed{552}$

 Mar 3, 2021
 #2
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The answer is 552

 Mar 3, 2021

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