Abstract:The main goal of this paper is to address the following problem: given a positive integer $n$, find the largest value $S(n)$ such that a square of edge length $S(n)$ in the Euclidean plane can be covered by $n$ unit squares. We investigate also the variant in which the goal is to cover only the boundary of a square. We show that these two problems are equivalent for $n \leq 4$, but not for $n=5$. For both problems, we also present the solutions for $n=5$.
From: Zsolt Langi Dr. [view email]
[v1]
Fri, 23 Jan 2026 08:11:17 UTC (565 KB)
[v2]
Tue, 28 Apr 2026 12:14:06 UTC (567 KB)
[v3]
Fri, 29 May 2026 09:31:13 UTC (567 KB)
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