My first impression of this (and the post that I made in response to the claim) was that it sounds an awful lot like the Friday the 13th claim which I'd looked at before.
But this isn't quite the same problem, although it sounds the same at first. The first distinction is that there is always exactly one December 25th in a year. The number of Fridays falling on 13ths ranges from one to three.
However the result ends up being much the same. In the normal 28 year cycle of calendars, December 25th falls evenly on each of the seven days of the week.
Running through the actual calenders (Unix 'cal' and 'grep'), over the 400 years from 1800 through 2199 yields:
So, even over the really long term, this claim is false.
Unlike the Friday the 13th case, the calendar order perterbation in this case left three weekdays tied for first place and two tied for last place.
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Copyright 1997, Drew Lawson.
[Last updated: 18 April 1997]