MATC Mathematics Club
Lecture #67

Madison Area Technical College
Madison, Wisconsin


Spring 2007 Presentation #67 (November 12, 2007)
by Professor John Kiltinen, Northern Michigan University

"The math behind the "15" puzzles and the other permutation puzzles"

Abstract: The familiar "15" puzzle that has 15 numbered tiles and one blank space on a 4 by 4 frame provides an entry point for some interesting mathematics that one typically encounters in about a junior-level course in abstract algebra. In this talk, the speaker will introduce ideas such as the parity of a scramble on this puzzle using his own puzzle software, and discuss why this is relevant to the solvability of the scramble. As time permits, the principles will be applied to variants of the standard puzzle which the software allows one to create.

Reassurance: This talk will not require knowledge of any advanced math.

But a Warning: The talk may create a need-to-know some advanced math in those who are susceptible to puzzles.  

Biography: John Kiltinen is a recently-retired professor of mathematics at Northern Michigan University. He joined the faculty there in 1971 following four years on the faculty at the University of Minnesota in Minneapolis. He earned his bachelor's degree at Northern Michigan University, and his Ph.D. in mathematics from Duke University. He is the author of numerous papers and a book about permutation puzzles and some puzzle software that was published by the Mathematical Association of America (MAA) in 2003. He has also recently taken up writing math parity songs. He has served a term on the MAA Board of Governors representing the Michigan Section of MAA. He spent a sabbatical leave in Finland in 1978-79, and was a Fulbright lecturer during this time. He has served on the Board of Trustees of Carthage College in Kenosha, Wisconsin. He has just completed his second season as the judge on "High School Bowl," a weekly television program on WNMU-TV.



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