DisCoMath Seminar: Mathematical Jigsaw Puzzles
DisCoMath Seminar
Mathematical Jigsaw Puzzles
Dr. Darren Narayan
Professor, School of Mathematics and Statistics
College of Science, Rochester Institute of Technology
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Abstract:
We consider the problem of tiling large rectangles using smaller rectangles with the prescribed dimensions 4x6 and 5x7. Problem B-3 on the 1991 William Lowell Putnam Examination asked "Does there exist a natural number L such that if m and n are integers greater than L, then an m x n rectangle may be expressed as a union of 4x6 and 5x7 rectangles, any two intersect at most along their boundaries?" Narayan and Schwenk showed in 2002 that all rectangles with length and width at least 34 can be partitioned into 4x6 and 5x7 rectangles. We investigate necessary and sufficient conditions for an m x n rectangle to be tiled with 4x6 and 5x7 rectangles, using techniques from algebra, combinatorics, and integer linear programming.
Intended Audience:
All are Welcome!
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