Generating Symmetric Crossword Grids for The New York Times Mini Puzzle

Abstract

A standard crossword puzzle grid contains words of at least three letters, has no completely black rows or columns, and is symmetric. These grids are combinatorial in nature, making them an interesting object of mathematical study. We present code that generates all possible 5×5 crossword grids under specific symmetry constraints, inspired by the format of The New York Times Mini crosswords. Our work builds on existing research by Cote and Merrill (2021) which gave a representation of crossword grids as bipartite graphs with a node for each word and an edge connecting any intersecting words. We construct crossword graphs for all 5x5 grids with various symmetries and study their graph theoretic features. This project contributes new results to the mathematical study of crossword puzzles by exploring non-traditional symmetries in puzzle grids (diagonal, horizontal, vertical) which have not previously been studied.