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
  1/1 

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
  http://mathforum.org/dr.math/