The month with exactly four of every weekday

Question

Most months contain five of at least one weekday.

Which month can contain exactly four of every weekday, four Mondays, four Tuesdays and so on through four Sundays? Under what condition does this happen, and how often?

Accepted Answer

February in a non-leap year. Why. Four of each of the seven weekdays makes 4 × 7 = 28 days exactly. The only month with 28 days is February in an ordinary year. Every other month has at least 29 days, so at least one weekday appears five times. How often. Three years out of every four, roughly. February has 28 days in every year that is not a leap year: all years not divisible by 4, plus century years not divisible by 400 (such as 1900 and 2100). In a leap year February has 29 days and one weekday appears five times, the weekday of 1 February. A tidy consequence. In a non-leap year, February'…

The month with exactly four of every weekday

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