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?
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?