A Closed Form for the Pulsar Sequence

TL;DR

This paper introduces a closed-form formula for the Pulsar Sequence, enabling the solution of Pulsar puzzles of any size by analyzing their properties derived from Latin-square-based puzzles.

Contribution

The paper presents the first explicit closed-form expression for the Pulsar Sequence, advancing the understanding of these Latin-square-based puzzles.

Findings

Derived a general formula for the Pulsar Sequence

Enabled solving Pulsar puzzles of arbitrary size

Analyzed properties of Pulsar puzzles

Abstract

In this paper, we study the Pulsar Sequence, an integer sequence derived from Latin-square-based Pulsar puzzles introduced by the Cracking the Cryptic YouTube channel. A Pulsar puzzle consists of two interlocked spirals of circled and uncircled squares, generating the Dual and Pulsar sequences, respectively. We investigate the properties of the Pulsar puzzle and focus our work on constructing the Pulsar Sequence, allowing us to solve a Pulsar puzzle of any size. A general formula to calculate any term of the Pulsar Sequence is proposed at the end of the paper.