Try this with a trapezium instead

Let SS be the set of lattice points (x,y)(x,y) with 1x20 1 \leq x \leq 20 and 1y30. 1 \leq y \leq 30. Let BSB \subseteq S be a subset of SS such that no set of 44 vertices in BB form a (non-degenerate) parallelogram. What is the largest possible number of elements in B?B?

Details and assumptions

A figure is degenerate if it has 0 area.

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