The Volokh Conspiracy - Some (I Hope Mildly Interesting) Pedantry About Day of Week Frequency:

A commenter in a recent thread writes, "So, if election day was the first Tuesday, it would occasionally (I can't do the math for how often) fall on Nov. 1--All Saints Day."

Another responds, "Nov. 1 is a Tuesday, on average, once every seven years (the same amount it's a Monday, or a Sunday, or a Friday). The math's not that hard. :)"

The second commenter is basically right, for all practical purposes. But he's not exactly right, at least if he's saying that it's precisely equally common for Nov. 1 to fall on each day of the week. Why? The answer is below.

(Show answer.)

	[Eugene Volokh, October 29, 2008 at 1:06pm] Trackbacks Some (I Hope Mildly Interesting) Pedantry About Day of Week Frequency: A commenter in a recent thread writes, "So, if election day was the first Tuesday, it would occasionally (I can't do the math for how often) fall on Nov. 1--All Saints Day." Another responds, "Nov. 1 is a Tuesday, on average, once every seven years (the same amount it's a Monday, or a Sunday, or a Friday). The math's not that hard. :)" The second commenter is basically right, for all practical purposes. But he's not exactly right, at least if he's saying that it's precisely equally common for Nov. 1 to fall on each day of the week. Why? The answer is below. (Show answer.) With the Gregorian calendar, every cycle of 400 years contains 97 leap years (every fourth year, minus years 100, 200, and 300). This means that the cycle ends up containing 400 x 52 weeks (364 days) + 400 extra days from the 365th day in each year + 97 extra days from the leap years. Since 497 is divisible by seven, that means each cycle contains an integer number of weeks, and Nov. 1, 2000 is thus on the same day of the week as Nov. 1, 2400. But the number of years, as opposed to days, in each cycle — 400 — isn't divisible by 7. It's thus not possible for each day of the week to be equally represented among Nov. 1s. (Hide answer.)