The Stable Matching Problem and Sudoku

Abstract

Are you having trouble getting married? These days, there are lots of products on the market for dating, from apps to websites and matchmakers, but we know a simpler way! That's right -your path to coupled life isn't through Tinder: it's through Sudoku! Read our fabulous paper where we explore the Stable Marriage Problem to help you find happiness and stability in marriage through math. As a bonus, you get two Sudoku puzzles with a new flavor.

Sequences of the Stable Matching Problem

“…This is sequence A185141 in the OEIS [5], where it is defined as "a(n) is the number of 'templates', or ways of placing a single digit within an n 2 by n 2 Sudoku puzzle so that all rows, columns, and n by n blocks have exactly one copy of the digit." This connection between preference profiles and Sudokus motivated the other paper we wrote [1].…”

“…In particular, each disjoint profile has exactly one pair of soulmates and one hell-pair. Such profiles correspond to entries in a disjoint-groups Sudoku [1], where in a particular place in a box, all digits are distinct across all the boxes. For example, the top-left corners of every box have distinct digits.…”

“…In our paper [1] we introduced a new type of Sudoku called joint-groups or JG Sudoku. In such a Sudoku every digit corresponds to a joint preference profile.…”

“…Example. Here is an example for a preference profile for n = 2 that allows two stable matchings: First man: [1,2], second man: [2, 1], first woman: [2, 1], second woman: [1,2]. There are two possible matchings, and both are stable.…”