1. ## Number Theory?

What is the most and the least number of Friday the 13ths you can get in one year? In a 12 month period? Proven mathematically...

2. Originally Posted by bearej50
What is the most and the least number of Friday the 13ths you can get in one year? In a 12 month period? Proven mathematically...
For a standard year (repeat this for a leap year) list which day number corresponds to the 13th of each month these are $d_1,\ ..,\ d_{12}$.

Now assume that the first friday in the year is on day $d_F$

Now for $d_F=1, .. \ 7$ count how many of $d_i-d_F,\ i=1,\ .. ,\ 12$ is divisible by $7$. The largest of these totals is the most Friday the 13th there can be in a standard year and the smallest is the fewest Friday the 13th there can be in a standard year.

Repeat for a leap year.

CB