Table des matières

Is there a Friday XIII every year, or are there years without? ^{1)} Are there years with lots and lots?^{2)} How many is the most in one year? ^{3)} The following simple table answers all these questions for you: I've already done the work. Just find the row that corresponds to the day of the week the first of January falls; the months with a Friday XIII are listed according to whether it is a leap year or not.

Months with a Friday XIII | ||
---|---|---|

1 Jan | Leap Year | Non-Leap Year |

Sun | January, April, July | January, October |

Mon | September, December | April, June |

Tue | June | September, December |

Wed | March, November | June |

Thu | February, August | February, March, November |

Fri | May | August |

Sat | October | May |

These days, with the availability of computing power, it is quite possible to “brute force” the problem; that is, write a little program, or even a simple spreadsheet, to calculate the fourteen possible calendars ^{4)}. However, I'm old enough to prefer finding the solution on the back of an envelope, and that is exactly what I did; I just recopied the result to this wiki.

- January 8 and 15 fall on the same day of the week as January 1, so January 13 falls two weekdays earlier, or five later, than January 1. January will have a Friday XIII if and only if the 1st falls on Sunday.
- When a month has 28 days, its 13th and the 13th of the following month will fall on the same weekday. When February has a Friday XIII in a non-leap year, March will have one, too.
- When a month has 29 days, as February does in non-leap years, the 13th of the following month will fall one weekday later.
- Similarly, when a month has 30 or 31 days, the 13th of the following month will fall respectively 2 and 3 weekdays later.
- The weekdays cycle, i.e. +8 is equivalent to +1 : a cycle of 7, returning to the same weekday, then advancing one.

With these rules, one can construct a table of the off-set to the weekday on which the 13th falls in each month relative to the weekday of January 1.

13th of… | Non-Leap | Leap |
---|---|---|

January | +5 | +5 |

February | +1 | +1 |

March | +1 | +2 |

April | +4 | +5 |

May | +6 | 0 |

June | +2 | +3 |

July | +4 | +5 |

August | 0 | +1 |

September | +3 | +4 |

October | +5 | +6 |

November | +1 | +2 |

December | +3 | +4 |

Reading this table, one sees, for instance that in leap years, May 13th falls on the same weekday as January 1, and in non-leap years August 13th does (instead). So if January 1st falls on a Friday, there will be a Friday XIII in May (leap years) or August (non-leap years). The other offsets are converted in the same way :

- ”+1” will correspond to a Friday XIII if January 1 fell on Thursday.
- ”+2” will correspond to a Friday XIII if January 1 fell on Wednesday.
- etc.

An earlier treatment of this topic is Friday XIII on one of my blogs; I hope this one is an improvement. I've also written Delocalization and Globalization of Holidays about “when does a year start.” Then there is a treatment much like to one above applied to Public Holidays in France.

Another question came up: what year might that have been? Given an invitation for an event on “Saturday, April 26th,” for instance, might it (if correct, of course) have been from last year?

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