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 <firstname.lastname@example.org>. 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.