Friday the 13th

Why does Friday the 13th occur every year?



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A week is 7 days, a month may be 28, 30 or 31 (and 29 in a leap year). Since these numbers are coprime (apart from 7 and 28), the weekday for a 13th changes from one month to the next. Over the course of a year, it falls on different days in different months and each weekday is represented. Curiously, though, it is more often Friday than otherwise. In a typical 400 year period, the proportion of Friday 13ths is 0.1444... rather than 1/7 which is 0.142857... The reason for choosing 400 years is that a century is not a leap year unless it is divisible by 400.