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Full-Text Articles in Physical Sciences and Mathematics
Which Chessboards Have A Closed Knight's Tour Within The Rectangular Prism?, Joseph Demaio, Mathew Bindia
Which Chessboards Have A Closed Knight's Tour Within The Rectangular Prism?, Joseph Demaio, Mathew Bindia
Faculty and Research Publications
A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. In 1991 Schwenk completely classified the m x n rectangular chessboards that admit a closed knight's tour. In honor of the upcoming twentieth anniversary of the publication of Schwenk's paper, this article extends his result by classifying the i x j x k rectangular prisms that admit a closed knight's tour.
Closed Knight's Tours With Minimal Square Removal For All Rectangular Boards, Joseph Demaio, Thomas Hippchen
Closed Knight's Tours With Minimal Square Removal For All Rectangular Boards, Joseph Demaio, Thomas Hippchen
Faculty and Research Publications
A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. In 1991 Schwenk completely classified the rectangular chessboards that admit a closed knight's tour. For a rectangular chessboard that does not contain a closed knight's tour, this paper determines the minimum number of squares that must be removed in order to admit a closed knight's tour. Furthermore, constructions that generate a closed tour once appropriate squares are removed are provided.
An Exploratory Overview Of Teaching Computer Game Development, Mario Guimaraes, Meg C. Murray
An Exploratory Overview Of Teaching Computer Game Development, Mario Guimaraes, Meg C. Murray
Faculty and Research Publications
The computer game industry has exploded reaching sales of several billion dollars a year and, consequently, a majority of college students are familiar with the gaming environment. In fact, videogame development has been cited as one way to motivate students to explore the world of Computer Science. However, most videogames are extremely complex computer programs created by a team of developers including programmers and graphic artists and represent thousands of hours of work. Fortunately there are software tools available that provide a way for simple computer games to be created fairly easily using a building block approach. This paper discusses …
Which Chessboards Have A Closed Knight's Tour Within The Cube?, Joseph Demaio
Which Chessboards Have A Closed Knight's Tour Within The Cube?, Joseph Demaio
Faculty and Research Publications
A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. When the chessboard is translated into graph theoretic terms the question is transformed into the existence of a Hamiltonian cycle. There are two common tours to consider on the cube. One is to tour the six exterior n x n boards that form the cube. The other is to tour within the n stacked copies of the n x n board that form the cube. This paper is concerned with the latter. In this paper …