The Mondrian Puzzle: A Bound Concerning the M(n) = 0 Case

2020/06/13 by O'Kuhn, Cooper, Fellman, Todd
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2006.12547

Abstract

In response to the Numberphile video regarding the Mondrian Puzzle https://www.youtube.com/watch?v=49KvZrioFB0, we provide a lower bound on how many integers less than a given threshold x satisfy M(n) ≠ 0 where M(n) is the quantity in which the Mondrian Puzzle is interested, i.e. the minimal difference in area between the largest and smallest rectangle in a set of incongruent, integer-sided rectangles which tile an n by n square.

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