There is at least one Friday the 13th every year.

Complete Solution:
There are 14 different calendars. There are seven possible calendars for non-leap years: one with January 1 on each day of the week. Leap years give seven more calendars, for a total of 14. For example, if January 1 is on a Wednesday, you have the following list:

January 1
January 13
February 1
February 13
March 1
March 13
April 1
April 13
May 1
May 13
June 1
June 13

Wednesday
Monday
Saturday
Thursday
Saturday
Thursday
Tuesday
Sunday
Thursday
Tuesday
Sunday
Friday

Because June 13 is a Friday, you can stop. The chart below shows the total number of Friday the 13ths for all 14 calendars.

 When January 1st is on Non-leap Year months with a Friday the 13th Leap Year months with a Friday the 13th Monday April, July September, December Tuesday September, December June Wednesday June March, November Thursday February, March, November February, August Friday August May Saturday May October Sunday January, October January, April, July

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