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 $\displaystyle d_1,\ ..,\ d_{12}$.
Now assume that the first friday in the year is on day $\displaystyle d_F$
Now for $\displaystyle d_F=1, .. \ 7$ count how many of $\displaystyle d_i-d_F,\ i=1,\ .. ,\ 12$ is divisible by $\displaystyle 7$. 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