Consider dates of the form *YY-MM-DD hh:mm*. Some puzzles are about such dates containing one of each digit 0 to 9. This isn’t one of them. Let’s go the other way. In 2011, there was the date 11-11-11 11:11. That is using only one of the digits.

How about two? Call them *a* and *b*, and let *a* be less than *b*. How many pairs (*a*, *b*) are there where there is at least one valid date of the form *YY-MM-DD hh:mm* containing at least one of each of *a* and *b*, and what are those pairs? Since *hh* can be expressed as 1 to 12 or 0 to 23, answer for both possibilities.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. **The deadline is Wednesday, August 6, 2014 at noon Pacific Time.** I will post the answer shortly after.