How many two digit numbers have one odd digit and one even digit?

So there are 45 positive 2 digit numbers with one odd and one even digit, starting with 10 and going up to 98. There are 90 positive 2 digit numbers, from 10 to 99. Of these, 50 (from 10-19 up to 90-99) start with an odd digit and 40 (from 20-29 up to 80-89) start with an even digit. Of the 50 that start with an even digit, half of them (25) have an odd second digit, and of the 40 that start with an even digit, 20 have an odd second digit. So there are 45 positive 2 digit numbers with one odd and one even digit, starting with 10 and going up to 98.

For each of these, there is a negative counterpart. So there are a total of 90 when both positive and negative numbers are considered.

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