# Friday 13

Prove that there is at least one Friday the 13th in some month during each year.

Prove that there are at most three Friday the 13ths any given year.

Hint: Number the days of the year from 1 through 365 (or 366). Determine which days would be the 13th of the successive months. Try a spreadsheet . . . The problem can be done, however, with a simple table of 12 lines, one for each month, where the number entered corresponds to the 13th of each month. x

Fox news reported on January 13th 2012 that there were to bethree months in 2012 with Friday the 13th. Correct. We were to a Friday 13th in April 2012 and again in July 2012.

What is the next year for which we will have 3 months with a Friday 13th? Fox News claimed it was 2040. Are they correct?

Related Problem

Joe Hooten, Professor Emeritus at the University of Georgia, observed that in 1998 both February and March had a Friday the 13th. That is, there was a Friday the 13th in two consecutive months.

In what years will this occur again?

Is there a cycle that can be specified for determining the years in which there will be two consecutive months with Friday the 13th?