Friday the 13th – Non 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 1 4 5 6 0 1 13-Mar 72 2 1 4 5 6 0 1 13-Apr 103 5 4 0 1 2 3 4 13-May 133 0 6 2 3 4 5 6 13-Jun 164 3 2 5 6 0 1 2 13-Jul 194 5 4 0 1 2 3 4 13-Aug 225 1 0 3 4 5 6 0 13-Sep 256 4 3 6 0 1 2 3 13-Oct 286 6 5 1 2 3 4 5 13-Nov 317 2 1 4 5 6 0 1 13-Dec 347 4 3 6 0 1 2 3

This table is for a year that is a non leap year.  Using mod 7 we can see from the above table which months will have a Friday the 13th.  The value of 6 represents the value 6 mod 7 and this value shows the months where the 13th falls on a Friday.  We can see that for a year in which January 1 falls on a Thursday, there will be three months that have a Friday the 13th and that for these years, there will be back to back months, February and March, where this will occur.  This is the only time that this will happen.  Since February in non leap years has 28 days, which is an even multiple in mod7, March will have the same dates on the same days as does February.  Since all other months are either 30 or 31 days, there will be a remainder in mod 7, and successive months will have the 13th on a different day than the preceding month. The starting day for the next year’s calendar in a non leap year will be the previous year’s starting day plus 1.  This table was made with Excel and used the formula feature that calculated the mod 7 values shown in the table.