Latin Puzzles

TL;DR

This paper extends Latin squares to Latin boards, introducing partial Latin boards and puzzles, including new Sudoku variants, and discusses methods for solving and measuring their difficulty, emphasizing constraint programming approaches.

Contribution

It generalizes Latin squares to Latin boards and introduces new puzzle variants, along with methods for solving and assessing their difficulty.

Findings

Introduction of partial Latin boards and puzzles

Examples of new Sudoku variants like Sudoku Ripeto and Custom Sudoku

Discussion on constraint programming methods for solving Latin puzzles

Abstract

Based on a previous generalization by the author of Latin squares to Latin boards, this paper generalizes partial Latin squares and related objects like partial Latin squares, completable partial Latin squares and Latin square puzzles. The latter challenge players to complete partial Latin squares, Sudoku being the most popular variant nowadays. The present generalization results in partial Latin boards, completable partial Latin boards and Latin puzzles. Provided examples of Latin puzzles illustrate how they differ from puzzles based on Latin squares. The examples include Sudoku Ripeto and Custom Sudoku, two new Sudoku variants. This is followed by a discussion of methods to find Latin boards and Latin puzzles amenable to being solved by human players, with an emphasis on those based on constraint programming. The paper also includes an analysis of objective and subjective ways to measure the difficulty of Latin puzzles.