MATC Mathematics Club
Lecture #130

Madison Area Technical College
Madison, Wisconsin

Fall 2013 Presentation #129 (November 15, 2013)

Professor Kenneth Price, UW-Oshkosh

"Secret Message Arrowgrams"

Abstract: An arrowgram is a type of mathematical puzzle consisting of letters connected by arrows. The arrows point from one letter to another. Some arrows are labeled with numbers and a rule based on transitivity is used to label the rest of the arrows. To describe the transitivity rule we say vertices X, Y, and Z form a transitive triple if there are arrows from X to Y, from Y to Z, and from X to Z. The arrow from X to Z is the hypotenuse. The arrows from X to Y and from Y to Z are the legs. We require the sum of the numbers on the legs to equal the number on the hypotenuse in every transitive triple. Arrowgrams also contain secret messages. The words are formed by pairs of letters which stand for the arrows. The puzzle is solved when every arrow is labeled with a number and the secret message is revealed. This talk will cover answers to some mathematical questions related to constructing and solving arrowgrams. You will also have the chance to solve some arrowgrams on your own.


Dr. Ken Price, Associate Professor of Mathematics, UW-Oshkosh, invented Arrowgrams as a way to communicate aspects of his research in algebra to non-mathematicians. Today his students create their own Arrowgrams as part of linear algebra and group theory classes. Price also helped create Face Off,  a student-centered math game show played at conferences around Wisconsin



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