Finding the Year's Share in Day-of-Week Calculations

TL;DR

This paper reviews and introduces methods for calculating the year share in day-of-week algorithms, including a new 'Parity Minus 3' method, with simplified correctness proofs and categorization of techniques.

Contribution

It presents a new year share calculation method, 'Parity Minus 3', and offers a comprehensive categorization and simplified proofs for existing and new methods.

Findings

Introduction of the 'Parity Minus 3' method

Simplified proofs of correctness for various methods

Categorization of year share computation techniques

Abstract

The dominant part in the mental calculation of the day of the week for any given date is to determine the year share, that is, the contribution of the two-digit year part of the date. This paper describes a number of year share computation methods, some well-known and some new. The "Parity Minus 3" method, in particular, is a new alternative to the popular "Odd+11" method. The paper categorizes the methods of year share computation, and presents simpler proofs of their correctness than usually provided. Keywords and phrases: day of the week, calendar algorithms, doomsday method, first Sunday algorithm, mental arithmetic, year share