Can there be a month with 6 Mondays? (or 6 of any other days?) This year, this month (November) we've 5 Mondays so I get 5 pay checks on 2nd, 9th, 15th, 22nd, 29th (which feels very good - I get paid one extra check :-).
I wonder if it's possible some years to have 6 Mondays? I haven't seen it but I wonder if there will be such year?
If Monday is not possible, then is any other week day possible to happen 6 times in one month?
(I'm mathematics enthusiast, no deep knoweldge - thanks!)

Mathematically, no it can't.
Practically, however, yes it can.
The calendar is defined by law, and there is precedent for the calendar being changed. In September 1752, Great Britain and the British Empire switched from the Julian to the Gregorian calendar, thereby skipping 3-13 September. This month only had 2 Mondays.
If dates can be removed by a law, they can also be added by law. If a country decided to switch the other way, right now, having already had 4 Mondays this month (today is 27 November 2015, Gregorian), we'd jump back to the 14th, and have two more Mondays (Julian and Gregorian weekdays are the same - Today is Friday the 14th Julian, Friday 27 Gregorian).
The Julian calendar is rarely used now, it drifts relative to the tropical year (that is, the day that the sun crosses the equator mid-autum(fall)/mid-spring keeps moving earlier and earlier).
