Crossing numbers — Turán's brickyard

About this app

How few crossings does a drawing need in which every point is joined to every other? Drag vertices, flip arcs, let it search: at best the counter lands on the Harary–Hill or Zarankiewicz formula. With straight edges a gap remains from K₈ on; the two-page drawing hits the formula exactly. Result from github.com/openai/math (family 165, Lean-formalised).

Subject: Open problems, solved by AI

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