Over on the (inexplicably login-walled) site “NewEnigma,”
Keith Austin writes:


  Draw a 4-by-4 grid. Colour each square red or blue. Select any square, S, and write 1 in it.
Then write 1 in every square you can reach from S by a series of moves, where each move is from
a square to an adjacent, horizontally, vertically, or diagonally, square of the same colour […]


In brief: What is the maximum number of queenwise-connected monochromatic regions you
can make by coloring each square of an \(n\times n\) grid either red or blue?

Authored by Arthur O'Dwyer, Quuxplusone offers  explorations of C++ programming language features, standard library design, and modern C++ development practices. Readers can delve into advanced topics such as template metaprogramming, design patterns, and effective use of language features. Additionally, they can learn about best practices for writing efficient and maintainable C++ code, optimizing performance, and leveraging the latest language standards.

Arthur O'Dwyer

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.

Colourfields