The plane is partitioned into congruent regular hexagons. Of these hexagons, some $1998$ are marked. Show that one can select $666$ of the marked hexagons in such a way that no two of them share a vertex.
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Tags: combinatorics, geometry, combinatorial geometry
The plane is partitioned into congruent regular hexagons. Of these hexagons, some $1998$ are marked. Show that one can select $666$ of the marked hexagons in such a way that no two of them share a vertex.