# Friday the 13th

I was looking at the schedule for the next year, there is a possibility that my first lecture will be on Friday the 13th. It got me doing a little back of envelope calculation to see how often does the 13th fall on a Friday.

I got this little sequence by calculating mod 7.
Jan – 0 ; Jul – 6
Feb – 3 ; Aug – 2
Mar – 3 ; Sep – 5
Apr – 6 ; Oct – 0
May – 1 ; Nov – 3
Jun – 4 ; Dec – 5

So assuming the date you want falls between 1-28 and it is not a leap year, the second and fourth column gives you the day on which it will fall on (modulo 7 of course.)

Example, the 13th falls on Friday in January. In Febuary it will be displaced by 3 days and falls on a Monday, in March it’s still 3 and falls on Monday again, in April it’s 6 which is a Thursday and so on. The chart tells you that we get another Friday the 13th in October. It fact, since 0-6 appears at least once, we always have a Friday the 13th in every (non-leap) year. And the worst you can do is to have the 13th falling on a Tuesday in January, then you’ll get a Friday the 13th on Febuary, March and November. This happens in 2009.

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### 2 Responses to Friday the 13th

1. splineguy says:

I like this. By the same reasoning, the sequence for the leap year is 0, 3, 4, 0, 2, 5, 0, 3, 6, 1, 4, 6. This means that if, in a leap year, January has a Friday the 13th, then so will April and July. This happens in 2012.