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Counting Friday the 13ths or Other Dates in a Year

Date: 12/17/2003 at 22:15:59
From: Nathan
Subject: friday the 13th

What is the greatest possible number of Friday the 13ths that can
occur in a year?

Date: 12/17/2003 at 22:22:56
From: Doctor Ian
Subject: Re: friday the 13th

Hi Nathan,

There's no formula, really, but basically, the idea is this.  Let's
say that January 1st falls on a Monday: 

  Mon   Tue   Wed   Thu   Fri   Sat   Sun

There are 31 days in January, which means that the 8th, 15th, 22nd,
and 29th will also fall on Monday.  The 30th will be a Tuesday, and
the 31st will be a Wednesday.  So February 1 will fall on a Thursday: 

  Mon   Tue   Wed   Thu   Fri   Sat   Sun
  1/1               2/1 

If you continue this for the rest of the months, you'll find that 
you'll never get more than 3 months in the same day column... but 
you'll get at least one month in each column.  

Why does this matter?  Well, if you change all the x/1's to x/13's,
you get the same table!  Which means that you can't get more than 3
Friday the 13ths in a single year... or fewer than 1. 

Does this help? 

- Doctor Ian, The Math Forum 
Associated Topics:
Elementary Calendars/Dates/Time
Middle School Calendars/Dates/Time

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