by
Jim Wilson
Let's start by number the days of the year 1 to 365 for non-leap years; 1 to 366 for leap years. Then it is quite easy to accumulate a list to enumerate which day of the year corresponds to the 13th of each month. For example January 13 is the 13th day of the year, February 13 is the 44th day of the year, March 13 is the 72nd day (in non-leap years) or the 73rd day (leap years).The week is seven days long and so counting off by 7s and keeping the remainders could give us a way of telling which day of the week each of these occurred IF we knew what day of the week January 1 was on.
Non-Leap Year ..................................Leap Year
| January | 13 | 6 | 13 | 6 |
| February | 44 | 2 | 44 | 2 |
| March | 72 | 2 | 73 | 3 |
| April | 103 | 5 | 104 | 6 |
| May | 133 | 0 | 134 | 1 |
| June | 164 | 3 | 165 | 4 |
| July | 194 | 5 | 195 | 6 |
| August | 225 | 1 | 226 | 2 |
| September | 256 | 4 | 257 | 5 |
| October | 286 | 6 | 287 | 0 |
| November | 317 | 2 | 318 | 3 |
| December | 347 | 4 | 348 | 5 |
Now, all that remains to to examine the cases for January 1 .
NON LEAP YEAR
| If January 1 is on | Then Fridays will be a | Friday 13th in the months of |
| Sunday | 6 | January October |
| Monday | 5 | April July |
| Tuesday | 4 | September December |
| Wednesday | 3 | June |
| Thursday | 2 | February March November |
| Friday | 1 | August |
| Saturday | 0 | May |
LEAP YEAR
If January 1 is on |
Then Fridays will be a |
Friday 13th in the months of |
| Sunday | 6 | January April July |
| Monday | 5 | September December |
| Tuesday | 4 | June |
| Wednesday | 3 | March November |
| Thursday | 2 | February August |
| Friday | 1 | May |
| Saturday | 0 | October |