#11 / 1-11-11: A Calendar Puzzler

I can't really remember when I first heard the idea that the condition of being "literate" has an analog in the mathematical arena, the condition of being "numerate."

If "illiteracy" is a problem to be concerned about, so is "innumeracy." Unfortunately, I have a tendency in that direction. Numbers aren't my forte.

When I reached today's date (1-11-11), I realized that for the second time this month, we are experiencing a day which (defined in at least one conventional calendar style) can be represented by repetitions of the same number, no other numbers appearing. The first date this year that met this test was, of course, 1-1-11. There will be, later on in the century, a 2-2-22, and there will be other such dates.

My puzzler question is this: for the current century (just starting from 1-1-11) how many days will there be where the date can be expressed (in the calendar style I have employed here) by repetitions of the same number, no other number appearing in the date?

I bet that truly "numerate" people could figure out a formula, or easily deduce the answer. I am not sure I can do that. Send me your solutions at gapatton@me.com. I'll publish them, right here, on another such date this year: 11-1-11.