Related papers: Multimedia Aplication for Solving a Sudoku Game
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…
We introduce an inductive logic programming approach that combines classical divide-and-conquer search with modern constraint-driven search. Our anytime approach can learn optimal, recursive, and large programs and supports predicate…
In this paper we will discuss scoring play games. We will give the basic definitions for scoring play games, and show that they form a well defined set, with clear and distinct outcome classes under these definitions. We will also show that…
In this paper, we introduce three different classes of undergraduate research projects that implement model building and integer programming. These research projects focus on determining and analyzing solutions to the game The Genius…
In this paper we study the Three Hat Problem which appeared in Puzzle Corner of the Technology Review magazine. This puzzle gives a scenario in which three players wearing hats are sitting together and each hat can be seen by everyone…
Many popular puzzle and matching games have been analyzed through the lens of computational complexity. Prominent examples include Sudoku, Candy Crush, and Flood-It. A common theme among these widely played games is that their generalized…
The purpose of this work is to explore a teaching methodology aimed at communicating topics and subjects not typically studied and analyzed in the (Italian) secondary school. We focused specifically on the use of videogames as a…
Humans excel in solving complex reasoning tasks through a mental process of moving from one idea to a related one. Inspired by this, we propose Subgoal Search (kSubS) method. Its key component is a learned subgoal generator that produces a…
We introduce the idea of an n-simplex graph and games upon simplicial complexes. We then define moves on a labeled graph and pose the problem of whether given two labelings of a graph it is possible to change one into another via these…
Our work has focused on support for film or television scriptwriting. Since this involves potentially varied story-lines, we note the implicit or latent support for interactivity. Furthermore the film, television, games, publishing and…
In the "Game about Squares" the task is to push unit squares on an integer lattice onto corresponding dots. A square can only be moved into one given direction. When a square is pushed onto a lattice point with an arrow the direction of the…
Based on a previous generalization by the author of Latin squares to Latin boards, this paper generalizes partial Latin squares and related objects like partial Latin squares, completable partial Latin squares and Latin square puzzles. The…
By first solving the equation $x^3+y^3+z^3=k$ with fixed $k$ for $z$ and then considering the distance to the nearest integer function of the result, we turn the sum of three cubes problem into an optimisation one. We then apply three…
This paper describes three different optimised implementations of playouts, as commonly used by game-playing algorithms such as Monte-Carlo Tree Search. Each of the optimised implementations is applicable only to specific sets of games,…
Automated testing of computer games is a challenging problem, especially when lengthy scenarios have to be tested. Automating such a scenario boils down to finding the right sequence of interactions given an abstract description of the…
Magic squares are well-known arrangements of integers with common row, column, and diagonal sums. Various other magic shapes have been proposed, but triangles have been somewhat overlooked. We introduce certain triangular arrangements of…
As the complexity and scope of games increase, game testing, also called playtesting, becomes an essential activity to ensure the quality of video games. Yet, the manual, ad-hoc nature of game testing leaves space for automation. In this…
We study an iteration approach to solve the coupled algebraic Riccati equations when they appear in general two player closed-loop type Nash differential games over an infinite time horizon. Also, we propose an effective algorithm for…
Positional games are a mathematical class of two-player games comprising Tic-tac-toe and its generalizations. We propose a novel encoding of these games into Quantified Boolean Formulas (QBFs) such that a game instance admits a winning…
We define the Sign Game as a two-player game played on a simple undirected mathematical graph $G$. The players alternate turns, assigning vertices of $G$ either $1$ or $-1$, and edges take on the value of the product of their endvertices.…