Methods for Accelerating Conway's Doomsday Algorithm (part 2)

TL;DR

This paper introduces a new, mentally easier method to compute a key component of the Doomsday Algorithm for determining the day of the week, specifically optimizing calculations for two-digit years.

Contribution

It presents a novel algebraic modification to the Doomsday Algorithm's calculation step, simplifying mental computation for two-digit years.

Findings

The new formula is easier to compute mentally.

It maintains accuracy while simplifying calculations.

Potential for faster mental calculations in calendar algorithms.

Abstract

We propose a modification of a key component in the Doomsday Algorithm for calculating the day of the week of any calendar date. In particular, we propose to replace the calculation of the required term: \lfloor \frac{x}{12} \rfloor + x \bmod 12 + \lfloor \frac{x \bmod 12}{4} \rfloor with -[ \frac{x+11(x \bmod 2)}{2} + 11 (\frac{x+11(x \bmod 2)}{2}\bmod 2)] \bmod 7 for a 2-digit input year x; Although our expression looks daunting and complicated, we will explain why it is actually easy to calculate mentally.