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Five Sundays, Mondays, and Tuesdays and Operations Research Training

A half dozen times in the past couple of weeks I have either been told, received an email, or otherwise ran across the following “fact”:

August 2010 has five Sundays, Mondays, and Tuesdays, and this won’t happen again for 823 years!

Wow!  That is pretty amazing.

It is also completely ridiculous and false.  May, 2011, for instance, has five Sundays, Mondays, and Tuesdays.  Even if the issue is an “August” with this structure, this occurs again in 2021 and 2027.  A moment’s thought reveals that you get five of those days anytime a month with 31 days starts on a Sunday, which has to be about 1/7 of them.   Since 7/12 of the months have 31 days, you would really expect about one month a year to have this structure, and that seems to be the case.

But, given all the repeats of this, there clearly are a lot of people who will buy into this sort of nonsense.  Why is that?  This really is a failure of mathematical training.  One reason we teach mathematics is to get people to think clearly and analytically on issues.  Ideally this would mean that people would immediately have an intuition that a result like this means that 31 day months (or August in particular) rarely start on a Sunday.  But experience shows that is not the case:  if the first day of some months is rarely a Sunday, surely I would have noticed that by now!  A quick check of any online calendar shows that the “fact” is false, and somebody has invented something ridiculous in order to see how many people can fall for this false meme.

Perhaps in operations research we have an advantage:  we are used to questioning the assumptions that go into models and looking carefully at the resulting solutions.  “Is this really linear?”  “If I assume X, what does that imply about Y?” “Does this answer make sense?”  Perhaps with a bit more OR training, urban myths will have to become a bit more sophisticated before they grab the public’s attention.