English

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

Number Theory 2020-06-24 v1

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 xx satisfy M(n)0M(n) \neq 0 where M(n)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 nn by nn square.

Keywords

Cite

@article{arxiv.2006.12547,
  title  = {The Mondrian Puzzle: A Bound Concerning the $M(n) = 0$ Case},
  author = {Cooper O'Kuhn and Todd Fellman},
  journal= {arXiv preprint arXiv:2006.12547},
  year   = {2020}
}