I guess it's time to explain this somewhat cryptic poll I posted a few weeks ago. The correct answer is 14.25% (exactly), or 57/400. For all days of the week, the answers would be: 58/400 Sun 56/400 Mon 58/400 Tue 57/400 Wed 57/400 Thu 58/400 Fri 56/400 Sat Why? 1/6

The Gregorian calendar uses years that are 365 days, but 366 days in years that are multiples of 4, except 365 in years that are multiples of 100, except 366 in year that are multiples of 400. See en.wikipedia.org/wiki/Gregor… So the pattern of year lengths is a 400 year cycle. 2/6

Given an arbitrary pattern of year lengths that form a 400 year cycle, there would be a one out of seven chance that the number of days in that 400 year cycle is a multiple of seven. 3/6

If the number of days in the 400 year pattern isn't a multiple of seven (the 6/7 chance), then matching of day-of-year to day-of-week would form a 2800 year cycle, as the 400 year cycle repeated itself on different days of the week, and probabilities above would be uniform. 4/6

However, in the *actual* 400 year cycle of the Gregorian calendar (which is close to matching the length of the mean tropical year), the number of days in the 400 year cycle *is* a multiple of seven. January 1, 2000 is a Saturday. So is January 1, 2400. And 2800, etc. 5/6