Friday the 13th


Show that for any year there must be at least one month and at most three months for which the 13th of the month falls on Friday.

Suggestion: Consider using a spreadsheet and numbering the days of the year by mod 7.


Observe that in 1998 both February and March have a Friday the 13th.

1. Prove that Friday the 13th can occur in two consecutive months only in February and March in a year that is not a leap year. On what day of the week must January 1 occur for February and March to have Friday the 13ths?

2. What is the next year in which this will occur again?

3. Is there a pattern or cycle by which you can determine which years between 2000 and 2100 that this will occur?

*Problem stated by Joe Hooten, Jr.