Counting Friday the 13ths or Other Dates in a YearDate: 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/ |
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