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A Closed Form for the Pulsar Sequence

Ryan Liu, Vadim Ponomarenko

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.

A Closed Form for the Pulsar Sequence

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.
Paper Structure (2 sections, 6 theorems, 9 equations)

This paper contains 2 sections, 6 theorems, 9 equations.

Table of Contents

  1. Introduction
  2. New Main Results

Key Result

Lemma 1

For each row $j$ with $2 \le j \le N$, the entry in the first column of a Pulsar puzzle is exactly one less than the entry in the last column of the same row.

Theorems & Definitions (12)

  • Lemma 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • proof
  • Theorem 5
  • proof
  • ...and 2 more