Friday the 13th – Leap Year

 Days to the 13th Sun Mon Tues Wed Thurs Fri Sat 13-Jan 13 6 0 1 2 3 4 5 13-Feb 44 2 3 4 5 6 0 1 13-Mar 73 3 4 5 6 0 1 2 13-Apr 104 6 0 1 2 3 4 5 13-May 134 1 2 3 4 5 6 0 13-Jun 165 4 5 6 0 1 2 3 13-Jul 195 6 0 1 2 3 4 5 13-Aug 226 2 3 4 5 6 0 1 13-Sep 257 5 6 0 1 2 3 4 13-Oct 287 0 1 2 3 4 5 6 13-Nov 318 3 4 5 6 0 1 2 13-Dec 348 5 6 0 1 2 3 4

This table is for a year that is a leap year.  This table shows the mod 7 value for the 13th of the month for each month.  If it occurs on a Friday the value will be 6, which corresponds to 6 mod 7.  The day at the top of the table is the day on which January 1 fell.  We can see from the table that each month has at least one Friday the 13th.  If January 1 falls on Sunday during a leap year, there will be three months that the 13th falls on Friday.  During a leap year there will be no consecutive months that have a Friday the 13th since February now has 29 days which is not an even multiple of 7.  Thus, the days in March will now fall on different days than those in February, which is the only possibility for having consecutive days in a non leap year.  After a leap year the starting day for the next year’s calendar will be the previous year’s starting day plus 2.  This table was also made on Excel using the mod 7 formula.