Friday the 13th

## First

Show that for any year there must be

at least onemonth andat most threemonths 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.

## Second*

Observe that in

1998both 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.