The day of the week (numbered according to for Sunday, for Monday, etc.) for a given day of the month ,
month , and year can be determined from the simple equation

where is the Floor Function, months are numbered

A more complicated form is given by

where for Sunday, for Monday, etc. and the numbers assigned to months, centuries, and years are given in the tables below (Kraitchik 1942, pp. 110-111).

Month | |

January | 1 |

February | 4 |

March | 3 |

April | 6 |

May | 1 |

June | 4 |

July | 6 |

August | 2 |

September | 5 |

October | 0 |

November | 3 |

December | 5 |

Gregorian | |

Century | |

15, 19, 23 | 1 |

16, 20, 24 | 0 |

17, 21, 25 | 5 |

18, 22, 26 | 3 |

Julian | |

Century | |

00, 07, 14 | 5 |

01, 08, 15 | 4 |

02, 09, 16 | 3 |

03, 10, 17 | 2 |

04, 11, 18 | 1 |

05, 12, 19 | 0 |

06, 13, 20 | 6 |

Year | Y | ||||||||

00 | 06 | 17 | 23 | 28 | 34 | 45 | 0 | ||

01 | 07 | 12 | 18 | 29 | 35 | 40 | 46 | 1 | |

02 | 13 | 19 | 24 | 30 | 41 | 47 | 2 | ||

03 | 08 | 14 | 25 | 31 | 36 | 42 | 3 | ||

09 | 15 | 20 | 26 | 37 | 43 | 48 | 4 | ||

04 | 10 | 21 | 27 | 32 | 38 | 49 | 5 | ||

05 | 11 | 16 | 22 | 33 | 39 | 44 | 50 | 6 | |

51 | 56 | 62 | 73 | 79 | 84 | 90 | 0 | ||

57 | 63 | 68 | 74 | 85 | 91 | 96 | 1 | ||

52 | 58 | 69 | 75 | 80 | 86 | 97 | 2 | ||

53 | 59 | 64 | 70 | 81 | 87 | 92 | 98 | 3 | |

54 | 65 | 71 | 76 | 82 | 93 | 99 | 4 | ||

55 | 60 | 66 | 77 | 83 | 88 | 94 | 5 | ||

61 | 67 | 72 | 78 | 89 | 95 | 6 |

**References**

Kraitchik, M. ``The Calendar.'' Ch. 5 in
*Mathematical Recreations.* New York: W. W. Norton, pp. 109-116, 1942.

Uspensky, J. V. and Heaslet, M. A. *Elementary Number Theory.* New York: McGraw-Hill, pp. 206-211, 1939.

Vardi, I. *Computational Recreations in Mathematica.* Reading, MA: Addison-Wesley, pp. 237-238, 1991.

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1999-05-26