Which weekday does the 13th land on most often?

Question

Superstitious people fear Friday the 13th. A mathematician might ask a more interesting question: over the long run, is the 13th of the month equally likely to fall on every weekday?

If not, which weekday hosts the 13th most often, and why is there any imbalance at all?

Accepted Answer

Friday, slightly more often than any other day. Why there is an imbalance at all. The Gregorian calendar repeats exactly every 400 years: the leap-year rule (every 4 years, except centuries, except every 400th year) has a 400-year period. In 400 years there are 400 × 365 + 97 leap days = 146,097 days. Divide by 7: 146,097 = 7 × 20,871 exactly. So 400 years is a whole number of weeks, and the calendar, weekdays included, repeats perfectly. Now, 400 years contain 4,800 months and therefore 4,800 thirteenths. Since 4,800 is not divisible by 7, the thirteenths cannot be spread evenly across the s…

Which weekday does the 13th land on most often?

Your answer

Discussion

Learn the concepts

Related questions