On the knight's tour on the fifteen puzzle

• Main Authors: Marcelino, Bernice Lhee C., Zarasate, Cherylle P.
• Format: text
• Language: English
• Published: Animo Repository 1997
• Subjects: Knight (Chess); Fifteen puzzle; Games; Mathematical recreations
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16448
• Institution: De La Salle University

This thesis presents the application of the knight's tour on the 15-puzzle. A 15-puzzle is made up of a 4-by-4 array wherein only 15 cells have numbers and the 16th cell is left as a blank. The numbers in the puzzle can be arranged by sliding it and a knight's tour on the puzzle is one wherein the numbers traces a knight's legal chess move. This paper also contains principles, that will aid in determining if a certain configuration in the 15-puzzle is legal or not, and propositions that are used in counting the knight's tour. All of the propositions, theorems and definitions in this research are lifted from the article The Knight's Tour on the Fifteen Puzzle by Spencer P. Hurd and David A. Trautman. The researchers provided basic definitions in group theory.