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.
2026-03-25 12:53:14.1774443194
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Calculate which day of the week a date falls in using modular arithmetic
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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.)