Methods for Accelerating Conway's Doomsday Algorithm (part 1)

TL;DR

This paper introduces a digit-based modification to the Doomsday Algorithm, simplifying mental calculation of the day of the week for any date by operating on individual digits of the year.

Contribution

It proposes a novel digit-based formula for the Doomsday Algorithm, enhancing mental calculation ease and efficiency.

Findings

The new formula simplifies mental calculations.

It maintains accuracy while reducing computational complexity.

The digit-based approach is more intuitive for mental math.

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 the term 2y + 10 \, (y \bmod 2) + z + \lfloor \frac{2 \, (y \bmod 2) + z}{4} \rfloor where x is an input 2-digit year; y is the tens digit of x; z is the ones digit of x; We argue the fact that our modification operates on individual base-10 digits makes the algorithm easier to calculate mentally.