Take n points, no two further apart than 1, and make the convex polygon they span as large as possible; every point must be a vertex of the hull.
Formal definition
ContainerNo container: the one global constraint is that no two points are further than 1 apart; coordinates are written inside [0, 1.5] × [0, 1.5]
SubmissionExactly n points
ConstraintsAll pairwise distances at most 1; every point a genuine hull vertex — on another pair's segment or inside does not count
ObjectiveMake the polygon area as large as possible; compared internally by twice the area, exactly
Getting a feel for it
Why the even cases are the hard ones
For odd n the regular polygon is provably optimal — nothing to contest. For even n it is NOT: Graham hexagon beats the regular one by about 4% of area. That is why only even n are offered here.
Where the frontier is
Regular polygons are optimal for odd n (Reinhardt 1922), so only even n are offered. On the even side n = 6, 8, 10 and 12 are proven (from Graham 1975 to Audet et al.); n ≥ 14 has only numerical best values and is open.
ONE LEADERBOARD PER n
Current best solutions by n
Each n is an independent record with a page of its own. Open any of them to inspect the current construction, then challenge it.