25. If the 13 th of any particular month falls on a Friday, we call it Friday the 13 th. It is known that Friday the 13 th occurs at least once every calendar year. If the longest interval between two consecutive occurrences of Friday the 13 th is $x$ months, find $x$.
25. Answer: 14 .
If 13th of January falls on a particular day, represented by 0, then the 13 th of February falls 3 days later, represented by $0+31 \equiv 3(\bmod 7)$.
Case 1: The consecutive two years are non-leap years.
\begin{tabular}{cccccccccccc}
\hline Jan & Feb & Mar & Apr & Mar & Jun & Jul & Aug & Sep & Oct & Nov & Dec \\
\hline 0 & 3 & 3 & 6 & 1 & 4 & 6 & 2 & 5 & 0 & 3 & 5 \\
1 & 4 & 4 & 0 & 2 & 5 & 0 & 3 & 6 & 1 & 4 & 6 \\
\hline
\end{tabular}

Case 2: The first year is a leap year.
\begin{tabular}{cccccccccccc}
\hline Jan & Feb & Mar & Apr & Mar & Jun & Jul & Aug & Sep & Oct & Nov & Dec \\
\hline 0 & 3 & 4 & 0 & 2 & 5 & 0 & 3 & 6 & 1 & 4 & 6 \\
2 & 5 & 5 & 1 & 3 & 6 & 1 & 4 & 0 & 2 & 5 & 0 \\
\hline
\end{tabular}

Case 3: The second year is a leap year.
\begin{tabular}{cccccccccccc}
\hline Jan & Feb & Mar & Apr & Mar & Jun & Jul & Aug & Sep & Oct & Nov & Dec \\
\hline 0 & 3 & 3 & 6 & 1 & 4 & 6 & 2 & 5 & 0) & 3 & 5 \\
1 & 4 & 5 & 1 & 3 & 6 & 1 & 4 & 0 & 2 & 5 & 0 \\
\hline
\end{tabular}

From these tables we see that the answer is 14 . The longest time period occurs when the Friday of 13th falls in July of the first year and in September of the second year, while the second year is not a leap year.