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Fun Fact: Friday the 13th is more common than many other days

The calendarepoch for the gregorian calendar (that the western world has been used since the 16th century) is 400 years. After that, the whole calendar repeats itself. It is exactly 146097 days in these 400 years. (Including all 4/100/400-rules.)

Out of these, there are 28 that are slightly more common than all others. One of those, is Friday the 13th, occuring 688 out of the 146097 days.

The least common day is a Wednesday the 31st, which happens 398 out of 146097 days.

Source, and more info

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  1. Algernon_Asimov
    (edited )
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    All the most-common days in this list fall in months that start with a Sunday the 1st (Friday the 13th is one of the Fridays in a month like this). Out of 4,800 months in the 400-year cycle this...

    All the most-common days in this list fall in months that start with a Sunday the 1st (Friday the 13th is one of the Fridays in a month like this). Out of 4,800 months in the 400-year cycle this is calculated on, 688 months start with a Sunday. The other days start months with slightly lower frequencies:

    • 684 months start with a Monday;
    • 687 months start with a Tuesday;
    • 685 months start with a Wednesday;
    • 685 months start with a Thursday;
    • 687 months start with a Friday;
    • 684 months start with a Saturday.

    I wonder if this is independent of the choice one makes for the first day of the cycle. If one had 7 versions of this cycle which each used a different day for the 1st of January in Year 1, would they all turn out the same? I have a hunch that they would not turn out the same. I have a gut feeling that, if one started the cycle with a Monday 1st January, one would find that the cycle contained 688 Mondays dated the 1st (and therefore 688 Fridays dated the 12th, instead of the 13th).

    Unfortunately, I don't have the programmatic skills to run a program to prove - or disprove - this hunch. I'm sure I could do it using a brute-force approach, but that might get a little tedious.


    EDIT: Ah-hah! I was right!

    I just spent half an hour brute-forcing this. I created a spreadsheet with 146,097 rows covering a 400-year cycle (with all the correct leap-year days). I've proven to myself that, if you change the day the cycle starts on, the frequency of months that start with each day of the week also changes. (Interestingly, each subsequent 400-year cycle starts on the same day of the week.)

    The linked data showing 688 months starting with a Sunday comes only if you start the 400-year cycle on a Monday. If I start the cycle on a Tuesday, then Monday 1st becomes the most common date that months start on (688 instances). Similarly, if I start the cycle on a Wednesday, then Tuesday 1st becomes the most common date that months start on. Whatever day of the week you start the cycle, the previous day is the most common day for starting months.

    Sorry, folks: this factoid is wrong.

    2 votes