Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1812.06778

Minuet: A method to solve Sudoku puzzles by hand

Carlos F. Daganzo
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper presents a systematic method to solve difficult 9 x 9 Sudoku puzzles by hand. While computer algorithms exist to solve these puzzles, these algorithms are not good for human's to use because they involve too many steps and require too much memory. For humans, all one can find in the literature are individual tricks, which used together in ad hoc ways can be used to solve some puzzles--but not all. To the author's knowledge, a systematic procedure made up of well-defined steps that can be carried out by hand and solve all puzzles has not been devised. This paper proposes one such technique--the "minuet" method. It is based on a new system of markings and a new way of simplifying the puzzles that can be easily carried out by hand--or by computer. The author has solved hundreds of puzzles of the most difficult kind ("evil" in Sudoku's parlance) and never found one that could not be solved. The average time to solve one of these puzzles is slightly over 1 hour. It is conjectured that this method can solve all well-posed 9 x 9 puzzles. The method's distinguishing feature is a "minuet" strategy that is applied when the puzzle cannot be further simplified with basic tricks. The strategy consists in concurrently developing two potential solutions, sometimes alone and sometimes in concert as if they were dancing a minuet.

Explore related subjects

cs.DMcs.DS

Keep this discovery

BibTeXRIS

Carlos F. Daganzo. 2018-12-13. Minuet: A method to solve Sudoku puzzles by hand. https://arxiv.org/abs/1812.06778

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

An FPTAS for Two-Machine Open-Shop Scheduling with a Single Unavailability Interval

We consider the two-machine open-shop scheduling problem in which one machine is unavailable during a fixed interval. We study the resumable setting: an operation interrupted by the unavailability interval may resume, without penalty, when the machine becomes available. The objective is to minimize the makespan. Although the problem is NP-hard and several approximation algorithms are known, whether it admits a fully polynomial-time approximation scheme (FPTAS) has remained open for two decades. We resolve this question affirmatively by giving the first FPTAS, thereby strengthening the previously known polynomial-time approximation scheme (PTAS). As an intermediate result, we develop a new pseudo-polynomial dynamic program with seven state dimensions, improving on the ten-dimensional formulation in the literature.

cs.DM↗
arXiv2026

Generalized Graph Search Trees

Graph search algorithms and their corresponding graph search trees are commonly used in algorithmic graph theory. In recent years, the recognition problem of these graph search trees has received significant attention. So far, the research has focused on two types of search trees: first-in trees that behave like BFS-trees and last-in trees that behave like DFS-trees. The search tree paradigms differ from each other by the parent a vertex is connected to. In first-in trees, it is the first visited neighbor, while in last-in trees it is the last neighbor visited before that vertex. Here, we will generalize these concepts of graph search trees by allowing every preceding neighbor of a vertex to be the parent. We study the complexity of the recognition problem of these generalized graph search trees. We present NP-completeness proofs for most searches. We also show that the problem is trivial for Generic Search and polynomial-time solvable for several searches on bipartite graphs and chordal graphs. We also study the question how fixing the start vertex influences the complexity of the problem.

cs.DM↗
arXiv2026

The exact asymptotic constant in the metric dimension of Jaccard space

Let $X$ be a finite set with $|X|=n$ and let $\mathrm{Jac}(a,b)=|a\,\triangle\, b|/|a\cup b|$ be the Jaccard distance on the power set $2^X$. Lladser and Paradise recently proved that the metric dimension of $(2^X,\mathrm{Jac})$ is $\Theta(n/\ln n)$, with the constant left open; their bounds are $(\ln 2)\,n/\ln n\lesssim \beta(2^X,\mathrm{Jac})\lesssim 2\ln(2e)\,n/\ln n$. We determine the constant: \[ \beta(2^X,\mathrm{Jac})=\frac{2n}{\log_2 n}\,(1+o(1))=(2\ln 2)\,\frac{n}{\ln n}\,(1+o(1)). \] The proof identifies the problem, on each ``slice'' of subsets of fixed cardinality, with the Erd\H{o}s--R\'enyi coin-weighing problem for a spring scale (the problem of \emph{detecting matrices}). The lower bound is the Erd\H{o}s--R\'enyi entropy argument applied to the middle slice; the upper bound follows from the explicit detecting families of Lindstr\"om and of Cantor and Mills, augmented by a single extra landmark that reveals cardinality.

cs.DM↗