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## Main Question or Discussion Point

If the Euclidean plane is partitioned into convex sets each of area A in such a way that each contains exactly one vertex of a unit square lattice and this vertex is in its interior, is it true that A must be at least 1/2?

If not what is the greatest lower bound for A?

The analogous greatest lower bounds for E

If not what is the greatest lower bound for A?

The analogous greatest lower bounds for E

_{n}obviously form a non increasing sequence (ordered by n). What is the value for E_{n}?