# Verifying Sudoku Puzzles

8-2022

Thesis

## Degree Name

Master of Arts in Mathematics

Mathematics

Jeremy Aikin

## Abstract

Sudoku puzzles, created by Meki Kaji around 1983, consist of a square 9 by 9 grid made up of 9 rows, 9 columns, and nine 3 by 3 square sub-grids called blocks. The goal of the puzzle is to be able to place the numbers 1 through 9 in every row, column, and block where no number is repeated in each row, column, and block. Imagine being given a completed Sudoku puzzle and having to check that it was solved correctly. You could just check all the rows columns and blocks (27 items), but is there a smaller number of checks that would suffice? In fact, what is the least amount of rows, columns, and blocks you would need to check? This question has been investigated by Emil Jeřábek, Tony Huynh, and others on various internet posts, where an answer has been posted, along with involved arguments that use a variety of mathematical tools. In this thesis, we investigate this question in the context of matroid theory and present a matroid theoretic solution by using the concept of circuits of a matroid.

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