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max no of circles in regular hexagon (I Soros Olympiad 1994-95 R1 9.6 10.4 11.3)

Source:

July 31, 2021
combinatorial geometrycircleshexagongeometry

Problem Statement

Given a regular hexagon, whose sidelength is 1 1 . What is the largest number of circles of radius 34\frac{\sqrt3}{4} can be placed without overlapping inside such a hexagon? (Circles can touch each other and the sides of the hexagon.)
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