Related papers: Unicity Concepts for Sudoku
This paper presents a comparative analysis of Sudoku-solving strategies, focusing on recursive backtracking and a heuristic-based constraint propagation method. Using a dataset of 500 puzzles across five difficulty levels (Beginner to…
In this paper we try to answer the question "What constitutes Sudoku difficulty rating across different Sudoku websites?" Using two distinct methods that can both solve every Sudoku puzzle, I propose two new metrics to characterize Sudoku…
Sumplete is a logic puzzle famous for being developed by ChatGPT. The puzzle consists of a rectangular grid, with each cell containing a number. The player has to cross out some numbers such that the sum of uncrossed numbers in each row and…
Symmetries in discrete constraint satisfaction problems have been explored and exploited in the last years, but symmetries in continuous constraint problems have not received the same attention. Here we focus on permutations of the…
A Sudoku puzzle often has a regular pattern in the arrangement of initial digits and it is typically made solvable with known solving techniques, called strategies. In this paper, we consider the problem of generating such Sudoku instances.…
Literature on Constraint Satisfaction exhibits the definition of several structural properties that can be possessed by CSPs, like (in)consistency, substitutability or interchangeability. Current tools for constraint solving typically…
Many of the famous single-player games, commonly called puzzles, can be shown to be NP-Complete. Indeed, this class of complexity contains hundreds of puzzles, since people particularly appreciate completing an intractable puzzle, such as…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
We introduce a large family of combinatorial objects, called standard puzzles, defined by very simple rules. We focus on the standard puzzles for which the enumeration problems can be solved by explicit formulas or by classical numbers,…
Magic squares are arrangements of natural numbers into square arrays, where the sum of each row, each column, and both diagonals is the same. In this paper, the concept of a magic square with 3 rows and 3 columns is generalized to define…
This paper is an up-to-date introduction to the problem of uniqueness versus non-uniqueness of infinite clusters for percolation on ${\mathbb{Z}}^d$ and, more generally, on transitive graphs. For iid percolation on ${\mathbb{Z}}^d$,…
We generalise the existence of combinatorial designs to the setting of subset sums in lattices with coordinates indexed by labelled faces of simplicial complexes. This general framework includes the problem of decomposing hypergraphs with…
The global approach to control systems which we have been pursuing in other work favours the study of dynamics achievable through control. It employs certain globally defined geometric objects and attempts to describe them in the general…
We study the concept of universal sets from the additive--combinatorial point of view. Among other results we obtain some applications of this type of uniformity to sets avoiding solutions to linear equations, and get an optimal upper bound…
We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…
The purpose of this review is to provide a brief overview of some recent conceptual developments about possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems.…
Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems (including uniqueness, recurrence, ergodicity,…
It is a fun game to complete a partial character table of a finite group. We show that one can reconstruct a missing row or column from a given table. The proof relies on deep properties of fully ramified characters. Moreover, we extend a…
In this paper, we exhibit the equivalence between different notions of unique range sets, namely, unique range sets, weighted unique range sets and weak-weighted unique range sets under certain conditions.\par Also, we present some…
Partial descriptions of the Universe are presented in the form of linear equations considered in the free (full, super) Fock space. The universal properties of these equations are discussed. The closure problem caused by computational and…