Prove that in each year, the 13th day of some month occurs on a Friday Prove that in each year, the 13th day of some month occurs on a  Friday.
No clue... please help!

Just brute force:
There is a calendar for a common year (i.e. a non-leap year) beginning on Sunday.
There is a calendar for a common year beginning on Monday.
There is a calendar for a common year beginning on Tuesday.
. . . and so on.  Seven calendars.  Then seven more for leap years.
Go through all 14 of them and observe that each has at least one Friday the 13th.  And some have two, and some have three, and none have more than three.
There may be no way to reach this conclusion except this kind of brute force, because the structure of the calendar (how many months, how many days in each month) is not defined by orderly rules.
