Calculate which day of the week a date falls in using modular arithmetic

modular-arithmetic number-theory calendar-computations

In Summer Wars the main character (he is a mathematician) calculates the day of the week of someone's birthday (19/07/1992 is Sunday). I know (very) basic modular arithmetic but I can't figure out how to do it. Can someone point me to the right direction? It seems fun to do.


Before the Doomsday method (see link in Theo Buehler's comment), there was a formula due to Gauss. A good write-up is Berndt Schwerdtfeger, Gauss' calendar formula for the day of the week, available at http://berndt-schwerdtfeger.de/cal/cal.pdf


The Zeller congruence is yet another method for reckoning the day of the week of a given date. Kim Larsen presents an implementation of a variant of the Zeller congruence in this article. (There is additional discussion of Larsen's formulation here.)

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