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We obtain partial progress towards answering the question of whether thequantity defined in the Mondrian Puzzle can ever equal 0. More specifically, weobtain a nontrivial lower bound for the cardinality of the set $\{n\leq x:M(n)\neq0 \}$ where $M(n)$ is the quantity appearing in the Mondrian Puzzle and$x$ is the usual quantity that one thinks of as tending to infinity. Moresurprisingly, we do so by use of number theoretic techniques in juxtapositionto the innately geometric nature of the problem.

The Mondrian Puzzle: A Connection to Number Theory