Vol. 12, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 3, 363–541
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN (electronic): 1944-4184
ISSN (print): 1944-4176
 
Author index
To appear
 
Other MSP journals
Solving Scramble Squares puzzles with repetitions

Jason Callahan and Maria Mota

Vol. 12 (2019), No. 2, 343–349
DOI: 10.2140/involve.2019.12.343
Abstract

A Scramble Squares puzzle consists of nine square pieces with half of an image on each side. To solve the puzzle the pieces are arranged in a 3 × 3 grid so that sides of adjacent pieces form complete images. A repetition is a half-image that appears more than once on a piece. Previous research uses a graph-theoretical approach to establish necessary and sufficient conditions for solutions without repetitions to 2 × 2 Scramble Squares puzzles. We use a similar approach to establish necessary and sufficient conditions for solutions with repetitions to 2 × 2 Scramble Squares puzzles.

Keywords
graph theory, directed graphs
Mathematical Subject Classification 2010
Primary: 05C75, 94C15
Milestones
Received: 20 December 2017
Revised: 20 March 2018
Accepted: 4 April 2018
Published: 8 October 2018

Communicated by Kenneth S. Berenhaut
Authors
Jason Callahan
Department of Mathematics
St. Edward’s University
Austin, TX
United States
Maria Mota
St. Edward’s University
Austin, TX
United States