Explain this about dates

Factual Questions
1

This year has 365 days and starts on a Wednesday.
This page shows that other years have the same number of days and start on the same day. We can see that they are in patterns of 11, 11 and 6 years. The next year the same will be 2014, 11 years, then 2025, and then 2031,
before the sequence repeats. Other years seem to use the same pattern.

What is the reason for this pattern?

I also noticed that after 1890, it was 12 years until the next one, and after 2098, it will be 12 until the next one. Any ideas about
why this is?

I know that the day a date is on in a year, is one day earlier than in the year before, except after a leap year when it is two days earlier. If it wasn’t for the leap year, you would expect that it would be every seven years, but is the leap year causing this 11, 11 and 6 year pattern?

2

If you had a leap year exactly every four then the pattern would repeat every 28 years but 3 out of 4 years ending in 00 are not leap so. . . the pattern repeats every 400 years.

3

Of course, as soon as I hit ‘submit’ I realised I was mistaken. The pattern repeats every 2800 years.

4

The only leap years divisible by 100 are also divisible by 400. Hence, 1900 wasn’t but 2000 and 1600 both were.

(This caused headaches semi-congruent to the Year 2000 Problem, as people went back to look over 40-year-old date code and found it horribly lacking. To this day, some applications still think 1900 was a leap year (or would if they were asked) and only got saved because the trivial algorithm (year % 4) works on 2000.)

5

sailor, I believe you were right the first time: the pattern repeats every 400 years.

Proof:

400 years = (365 x 400) + 97 = 146097 days;
146097 mod 7 = 0.

So 400 years contain an integral number of weeks.

Re the OP: notice, first of all, that 11 + 11 + 6 = 28, which is the first period sailor referred to. Also, the reason for the 11- vs. 12-day difference is that the periods beginning in 1890 and 2098 contain centenary years (1900 and 2100) that aren’t leap years, so it takes one more “extra” year to get back to where you started.

If you talk about individual days of the year, they actually repeat on a given day of the week in the pattern 11-6-5-6 (for example, Jan. 1 of this year was on a Wednesday, and so are Jan. 1 of 2014, 2020, 2025, and 2031). The page you’re referring to, though, is talking about year types; 2020 is not the same as the other ones, since it’s a leap year.