Which day of the week (Sunday, Monday, etc.) is the probability largest to fall on the 13th of a random month, in a random year?

Or is this probability the same for each day of the week?

(In reply to Solution by Penny)

In reply to:

"For 2004-2008, there will be 9 Sundays, 8 Mondays, 10 Tuesdays, 8 Wednesdays, 9 Thursdays, 8 Fridays and 8 Saturdays that fall on the 13th of the month.

For 2004-2013, there will be 18 Sundays, 16 Mondays, 19 Tuesdays, 17 Wednesdays, 16 Thursdays, 18 Fridays and 16 Saturdays that fall on the 13th of the month.

For 2004-1000000, there is no significantly more likely day. There will be 1710853 Sundays, 1710851 Mondays, 1710852 Tuesdays, 1710853 Wednesdays, 1710851 Thursdays, 1710853 Fridays and 1710851 Saturdays that fall on the 13th of the month. (Of course, by 1000000 AD, only Alan Greenspan will still be around to verify this)."

The figures for up to 2013 are correct; however those for years to a million are incorrect.  The days cannot be that evenly divided as in each 400-year period the distribution is the same:

687  685  685  687  684  688  684

And friday's 1-day advantage over its nearest competitors Sunday and Wednesday will build over time. Over the million years, it should grow to almost 2500 extra occurrences of Friday than Sunday.

Perhaps what went wrong was in using INTEGER rather than LONG. INTEGER can go only up to about 32,000 and then cycles around to something like -32,000, etc, so you're not getting the real year numbers in your comparison for leap year, and are in fact getting the same 64,000 (approx) years over and over again.  There might be other problems, as even this is a large enough time span for the 400-year cycle to be felt.  Perhaps because the year numbers go negative.  Try the same thing with the years limited to say 10,000.

BTW, as noted before, the inaccuracies of the Gregorian year relative to the tropical (seasonal) year are enough so that some calendar reform would take place much before 1,000,000 years (or even 10,000 years).

Posted by Charlie on 2004-08-13 14:10:15