2007 OIM Problems/Problem 6

Problem

Let $F$ be the family of all convex hexagons $H$ such that the opposite sides of $H$ are parallel, and any three vertices of $H$ can be covered with a strip of width 1. Find the smallest real number $l$ such that each of the hexagons of family $F$ can be covered with a strip of width $l$.

Note: A strip of width $l$ is the region of the plane included between two parallel lines that are at a distance $l$ (including both parallel lines).

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions