Arrowgrams: The Next Pencil and Paper Phenomenon
Abstract
Puzzles are a fascinating part of everyday life, and newspapers everywhere feature
crosswords, word jumbles, and Sudokus as a way to test and intrigue the human mind.
Arrowgrams are a new type of pencil and paper puzzle created by Dr. Kenneth Price
of the University of Wisconsin Oshkosh. In these puzzles, directed graphs, which
are a widely used physical element in both mathematics and computer science, are
partially labeled, and the goal of the puzzle solver is to complete the rest of the labeling
using the transitivity rule, which is a rule that resembles the Pythagorean Theorem.
After completing the rest of the labeling, the solver may then find a secret message
encoded in the puzzle. By analyzing arrowgrams using linear algebra, a puzzle creator
can determine exactly what arrows need to be labeled for the puzzle to be uniquely
solvable. A theorem is presented that relates which arrows need to be labeled for a
special kind of directed graph called a tournament directed graph.
Subject
Directed graphs
Linear algebra
Arrowgrams
Puzzles
Permanent Link
http://digital.library.wisc.edu/1793/70947Citation
Volume VIII, December 2013, pp. 74 - 86