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Family of hexagons

Source: Iberoamerican Olympiad 2007, problem 6

September 14, 2007
geometrytrigonometryrhombuscombinatorics unsolvedcombinatorics

Problem Statement

Let F \mathcal{F} be a family of hexagons H H satisfying the following properties: i) H H has parallel opposite sides. ii) Any 3 vertices of H H can be covered with a strip of width 1. Determine the least ℓ∈R \ell\in\mathbb{R} such that every hexagon belonging to F \mathcal{F} can be covered with a strip of width ℓ \ell. Note: A strip is the area bounded by two parallel lines separated by a distance ℓ \ell. The lines belong to the strip, too.
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