Why does every year contain at least one Friday the 13th and not more than three?

Answer 1

Yes. It occurs at least once every year (in fact, about/appx. every eight months). For example:

1993 - August

1994 - May

1995 - January & October

1996 - September & December

1997 - June

1998 - February, March & November

1999 - August

2000 - October

2001 - April & July

2002 - September & December

2003 - June

2004 - February & August

2005 - May

2006 - January & October

2007 - April & July

2008 - June

This is incorrect. Friday the 13th is on May 13, 2011, and the next occurance happens on January 13th, 2012.

Answer 2

Will Friday the 13th occur every year?

i decided i need a property for Fri the 13th to make my proof easier. i chose the fact that if Friday is the 13th, then Sunday is the 1st. From there, i set out to prove that every year, at least one Sunday will be the first of some month, thus proving the existence of Fri the 13th.

CLAIM: It doesn't matter what day the year starts on because no matter what day the year begins on, each day of the week is the first of some month (which would complete my proof). for this proof, i used modular arithmetic. its a lot more simple than it looks..

Let 0=Su, 1=M, 2=Tu, 3=W, 4=Th, 5=F, 6=Sa (so, I'm working in mod 7)

CASE 1: Non-Leap Year

Jan 1=0mod7

Feb 1=31=3mod7

Mar 1=31=3mod7

Apr 1=34=6mod7

May 1=36=1mod7

Jun 1=32=4mod7

Jul 1=34=6mod7

Aug 1=37=2mod7

Sep 1=33=5mod7

Oct 1=63=0mod7

Nov 1=31=3mod7

Dec 1=33=5mod7

This is the initial rotation of 1st's. Note that all of the numbers 0-6 (mod 7) are represented. This means that each day starts some month. CASE 2: Leap Year can also be studied based on CASE 1. Note that between Feb-Dec, which is what a Leap Year alters by one day, all of the numbers 0-6 are represented. Therefor, in a given year, Leap or Not, each day of the week falls on the first of some month, which implies that some month will always have a Friday the 13th. ■

Answer 3

See proof at Does_every_year_contain_at_least_one_Friday_the_13th

Addendum:

If you count the occurrences of each number in mod 7, you will know how many times Friday the 13th will occur at most or minimum. 3 comes up 3x, but let's not forget leap year. We'd get 0 3x, but to answer the question, it can happen at most 3x.

Let's see about a minimum... 1, 2, & 4 all come up just once, so 1x minimum.

There you have it: at most 3x, at least once.

Answer 4

because of the way the months line up.

There are 7 days in the week . It's given that the 13th will be on a Friday at least once

Answer 5

No. There is either one, two or three Friday the 13ths in any year.

Answer 6

It can be either, one, two or three, depending on the year.

Answer 7

There are several Friday 13ths in each year. In 2017 in January and October.