Determine the number of 6 digit positive integers such that at least one pair of consecutive digits differs by an odd number.

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I noticed that for an odd digit, then there are 4 choices for an even digit. For an even digit, there are 5 choices for an odd digit. There are 5 locations possible in the integer. What would be a good approach here?

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Hint: look for examples of $6$-digit integers where consecutive digits never differ by an odd number.