### Brain Teasers

# Friday the 13th

When's the next year when there won't be a Friday the 13th?

### Answer

Never.The 13th of each month will fall on different days, according to a complex pattern which takes several years to repeat, because of Leap Years. However, each day of the week comes up as the 13th within the first 9 or 10 months every year.

Assign A, B, C, D, E, F, & G randomly to Sun, Mon ... Sat.

If we assume, in a non leap year, that:

* 13 Jan is Day A, then

* 13 Feb is Day D,

* 13 Mar is Day D,

* 13 Apr is Day G,

* 13 May is Day B,

* 13 Jun is Day E,

* 13 Jly is Day G,

* 13 Aug is Day C,

* 13 Sep is Day F

Thus all seven possible days of the week have been used, within a 9-month period.

Similarly, in a leap year:

* 13 Jan is Day A, then

* 13 Feb is Day D,

* 13 Mar is Day E,

* 13 Apr is Day A,

* 13 May is Day C,

* 13 Jun is Day F,

* 13 Jly is Day A,

* 13 Aug is Day D,

* 13 Sep is Day G,

* 13 Oct is Day B,

Thus all seven possible days of the week have been used, within a 10-month period.

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## Comments

I did not get that!

Really, thats the best you could think of to say, I thought it was OK for a first teaser.

Attention everyone else, she is my friend and is really just trying to annoy me. Please post if you like or hate it

Attention everyone else, she is my friend and is really just trying to annoy me. Please post if you like or hate it

This is kind of cool!

u 2 r crazy i like this one its ok

A good teaser, but it requires a lot more thought than you suggest! The answer is right, but your use of probability is not correct - I have submitted a suggestion for a better explanation.

Keep up the good work!

Keep up the good work!

Assume it's not a leap year.

When a month starts on Sunday, it will have a Friday the 13th.

Monday, Thursday, Thursday, Sunday, Tuesday, Saturday, Monday, Tursday, Saturday, Tuesday, Thursday, Sunday.

As you see, no Wednesday.

2 days before Friday.

2 days before Monday, the day I started with. There will be no Friday the 13th.

The next non-leap year that starts on Saturday will not have a Friday the 13th.

When a month starts on Sunday, it will have a Friday the 13th.

Monday, Thursday, Thursday, Sunday, Tuesday, Saturday, Monday, Tursday, Saturday, Tuesday, Thursday, Sunday.

As you see, no Wednesday.

2 days before Friday.

2 days before Monday, the day I started with. There will be no Friday the 13th.

The next non-leap year that starts on Saturday will not have a Friday the 13th.

@Mathgeek007 - In a leap year that starts on a Saturday, October will have a Friday the 13th

Oops. Sorry i mis-read your comment "Non-leap year"

in a non-leap year that starts on a Saturday, May will have a Friday the 13th

When a non-leap year starts on a Monday the first day of each month (Jan-Dec) fall on

Mon,Thurs,, Thurs, Sun, Tues, Fri,

Sun, Wed, Sat, Mon, Thur, Sat

In a leap year starting on a Monday the 1st day of the months fall on

Mon, Thur, Thur, Mon, Wed, Sat

Mon, Thur, Sun, Tues, Fri, Sun

In both cases there is a least 1 month starting on each day of the week. So, if the starting day of the year is shifted there will still be at least one month starting on a Sunday meaning there will be at least one Friday the 13th in any year.

Mon,Thurs,, Thurs, Sun, Tues, Fri,

Sun, Wed, Sat, Mon, Thur, Sat

In a leap year starting on a Monday the 1st day of the months fall on

Mon, Thur, Thur, Mon, Wed, Sat

Mon, Thur, Sun, Tues, Fri, Sun

In both cases there is a least 1 month starting on each day of the week. So, if the starting day of the year is shifted there will still be at least one month starting on a Sunday meaning there will be at least one Friday the 13th in any year.

You beat me to post! Also, the year is 2022

There are only 14 possible distinctive calendars. One for each day Jan. 1 can start on for a non-leap year (7), and another set for leap year (7). If you look at each of these 14 possibilities, there is ALWAYS a year that has at least 1 month that will start on Sunday (resulting in Friday the 13th). Therefore, there will ALWAYS be a Friday the 13th in every year. It has nothing to do with probability.

Sorry, guys, every year MUST have a Friday 13th. Mathgeek - you need to check your logic, and others do, too. May 13, 2022 will be a Friday.

The answer is correct, but the reasoning is totally wrong, as this has nothing to do with probability. The theory of probability relies on events being random ... and this is not random.

The answer is correct, but the reasoning is totally wrong, as this has nothing to do with probability. The theory of probability relies on events being random ... and this is not random.

I got it right only because there has always been to be at least one Friday the 13th in my 56+ years of living. Some years more than others. Nice work!

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