MathDB

6

Part of 2007 IberoAmerican

Problems(1)

Family of hexagons

Source: Iberoamerican Olympiad 2007, problem 6

9/14/2007
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.
geometrytrigonometryrhombuscombinatorics unsolvedcombinatorics