Associated Topics || Dr. Math Home || Search Dr. Math

### Friday the 13ths in a Year

```
Date: 08/10/99 at 04:06:28
From: Stephanie Cole
Subject: Max number of Friday the 13ths in a year

How can I figure out the maximum number of Friday the 13ths there are
in one year? I know that 1998 had 3 because I looked at my mom's old
calendar. But why do some years have 2 or 3, and why do all years have
at least one?

Thank you. (I think your web site is great).
```

```
Date: 08/20/99 at 10:55:39
From: Doctor TWE
Subject: Re: Max number of Friday the 13ths in a year

Hi Stephanie -

The trick here is to figure out which months start on the same day of
the week. In a standard (non-leap) year, if January starts on a
Monday, then February starts on a Thursday, March also starts on a
Thursday, etc.

Since January has 31 days, it has 4 full weeks (28 days) plus 3 days.
Hence, February must start 3 weekdays later. Similarly, since February
has 28 days (4 weeks + 0 days,) March starts on the same weekday as
February. Continuing this pattern, you can see which months start on
the same days, and you can count how many months start on each day.
Remember to do the counts for both a standard year and a leap year!

If months (like February and March) start on the same weekday,
logically the 13th of those months will also fall on the same weekday
- which will, in certain years be a Friday. So whatever was the
highest count of months starting on the same weekday, that number is
the most Friday the 13th's there could possibly be.

Try counting them out and see what you come up with!

As a related aside, the average number of Friday the 13th's is
really quick to compute: There are 12 months (therefore 12 "13th's")
and 7 weekdays for them to fall on, so the average number of Friday
the 13th's in a year is 12/7, or about 1.714.

- Doctor TWE, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Puzzles

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search