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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.

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I actually teach this algorithm in my algorithms class; it's useful in real life to be able to do this! – Fixee Apr 20 '11 at 3:54
Dershowitz/Reingold is the go-to book for topics like these. – J. M. Apr 20 '11 at 4:56
I wonder if O’Beirne’s algorithm (sixthform.info/maths/?p=155) to find the date of Easter Sunday is based (at least partialy) on this one. – Américo Tavares May 12 '11 at 23:39

3 Answers

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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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I believe that this website is the easiest and fastest way to learn this.

http://www.terra.es/personal2/grimmer/

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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

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