Problem - 4252
Show that there is at least one Friday $13^{th}$ in any year, including any leap year.
This is equivalent to showing that every year, leap year included, has at least one Sunday the $1^{st}$ each month. Let's exam the days when the $1^{st}$ day of each month falls.
Regardless of whether it is a leap year or not, the $1^{st}$ day of each month includes all the residue classes of modulo $7$. This means at least one of them will be on Sunday. Hence, the claim holds.