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Covering the perimeter of rectangle with unit disks

Source: KoMaL A. 850

April 12, 2023
geometrycombinatorial geometryrectangle

Problem Statement

Prove that there exists a positive real number NN such that for arbitrary real numbers a,b>Na,b>N it is possible to cover the perimeter of a rectangle with side lengths aa and bb using non-overlapping unit disks (the unit disks can be tangent to each other).
Submitted by Benedek Váli, Budapest
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