Solution
Unlucky Thirteenths
Show the problem again
The Gregorian calendar repeats exactly every 400 years (146 097 days, which is a whole number of weeks). Over one complete 400-year cycle, on how many dates does the 13th of a month fall on a Friday? Give an integer.
Worked solution
Because 146 097 = 7 × 20 871, the weekday pattern repeats exactly every 400 years, so it suffices to count within one cycle (for example 2001 to 2400). The 4800 thirteenths do not fall evenly on the seven weekdays. Counting every month of every year gives 688 on Friday, 687 on Wednesday and on Sunday, 685 on Monday and on Tuesday, and 684 on Thursday and on Saturday. So Friday is the single most common day for the 13th, and the answer is **688**.
Source: Friday-the-13th frequency in the Gregorian calendar is a well-known calendar fact; this counting question written for AxiomIQ.