---
title: "Colourfields"
url: https://daily.dev/posts/colourfields-bflskiyju
source_url: https://quuxplusone.github.io/blog/2026/08/05/colourfields
type: article
source: "Arthur O'Dwyer"
published: 2026-08-05T20:06:07.679Z
updated: 2026-08-05T22:32:45.349Z
tags: ["graph-theory"]
reading_time: 2
upvotes: 0
comments: 0
language: en
---

> ## Documentation Index
> Fetch the complete documentation index at: https://daily.dev/llms.txt
> Use this file to discover all available pages before exploring further.

# Colourfields

**[Arthur O'Dwyer](https://daily.dev/sources/quuxplusone)** · 2 min read · 0 upvotes · 0 comments

## Summary

A mathematical puzzle exploring the maximum number of queenwise-connected monochromatic regions achievable by coloring squares of an n×n grid red or blue. The problem, originally posed on NewEnigma, asks for the largest 'score' (number of distinct color-connected regions) for 4×4 and 5×5 grids. Discussion on the SeqFan mailing list has produced a tentative sequence: 1, 2, 5, 6, 10, 12, 17, 19, 26, (28?)… with conjectured patterns for odd and even grid sizes.

## Full article

daily.dev links to this article rather than hosting it. Read it at the original source: <https://quuxplusone.github.io/blog/2026/08/05/colourfields>

## Similar posts on daily.dev

- [Solving the 3Blue1Brown String Probability Problem \(Without AI\)](https://daily.dev/posts/solving-the-3blue1brown-string-probability-problem-without-ai--thczbuec0) · Towards Data Science · 0 upvotes · 0 comments

---

Tags: [#graph-theory](https://daily.dev/tags/graph-theory)

[View this post on daily.dev](https://daily.dev/posts/colourfields-bflskiyju)