Related papers: Mathematical Definition and Systematization of Puz…
This work investigates the reasoning and planning capabilities of foundation models and their scalability in complex, dynamic environments. We introduce PuzzlePlex, a benchmark designed to assess these capabilities through a diverse set of…
Pattern-Based Constraint Satisfaction and Logic Puzzles develops a pure logic, pattern-based perspective of solving the finite Constraint Satisfaction Problem (CSP), with emphasis on finding the "simplest" solution. Different ways of…
Numberlink is a puzzle game in which players are given a grid with nodes marked with a natural number, $n$, and asked to create $n$ connections with neighboring nodes. Connections can only be made with top, bottom, left and right neighbors,…
Logical rules are a popular knowledge representation language in many domains, representing background knowledge and encoding information that can be derived from given facts in a compact form. However, rule formulation is a complex process…
Existing reasoning benchmarks for large language models (LLMs) frequently fail to capture authentic creativity, often rewarding memorization of previously observed patterns. We address this shortcoming with Sudoku-Bench, a curated benchmark…
Evolomino is a pencil-and-paper logic puzzle published by the Japanese company Nikoli, renowned for culture-independent puzzles such as Sudoku, Kakuro, and Slitherlink. Its name reflects the core mechanic: the polyomino-like blocks drawn by…
Algorithmic reasoning is a fundamental cognitive ability that plays a pivotal role in problem-solving and decision-making processes. Reinforcement Learning (RL) has demonstrated remarkable proficiency in tasks such as motor control,…
The mathematical aspects of the popular logic game Sudoku incorporate a significant number of the group theory concepts. In this note, we describe all symmetric transformations of the Sudoku grid. We do not intend to obtain a new strategy…
We propose the study of mathematical ludology, which aims to formally interrogate questions of interest to game studies and game design in particular. The goal is to extend our mathematical understanding of complex games beyond…
Solving Sudoku puzzles is one of the most popular pastimes in the world. Puzzles range in difficulty from easy to very challenging; the hardest puzzles tend to have the most empty cells. The current paper explains and compares three…
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…
Over the last decade, Sudoku, a combinatorial number-placement puzzle, has become a favorite pastimes of many all around the world. In this puzzle, the task is to complete a partially filled $9 \times 9$ square with numbers 1 through 9,…
Wataridori is a pencil puzzle that involves drawing paths in a rectangular grid to connect circles into pairs while satisfying several constraints. In this paper, we prove that deciding whether a given Wataridori puzzle has a solution is…
We introduce Pencil Puzzle Bench, a framework for evaluating large language model reasoning through pencil puzzles, a family of constraint-satisfaction problems closely related to NP-complete problems, with deterministic, step-level…
The success of Large Language Models (LLMs) in human-AI collaborative decision-making hinges on their ability to provide trustworthy, gradual, and tailored explanations. Solving complex puzzles, such as Sudoku, offers a canonical example of…
Sudoku is a widely popular $\mathcal{NP}$-Complete combinatorial puzzle whose prospects for studying human computation have recently received attention, but the algorithmic hardness of Sudoku solving is yet largely unexplored. In this…
The mathematical structure of the widely popular Sudoku puzzles is akin to typical hard constraint satisfaction problems that lie at the heart of many applications, including protein folding and the general problem of finding the ground…
Large Reasoning Models (LRMs) have demonstrated impressive performance on complex tasks, including logical puzzle games that require deriving solutions satisfying all constraints. However, whether they can flexibly apply appropriate rules…
Jigsaw puzzle solving, the problem of constructing a coherent whole from a set of non-overlapping unordered visual fragments, is fundamental to numerous applications, and yet most of the literature of the last two decades has focused thus…
An unconstrained crossword puzzle is a generalization of the constrained crossword problem. In this problem, only the word vocabulary, and optionally the grid dimensions are known. Hence, it not only requires the algorithm to determine the…