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Problem 189
If is finitely coloured then must there exist some colour class which contains the vertices of a rectangle of every area?
Source: erdosproblems.com/189
- Geometry
- Ramsey theory
Status
Solved, DisprovedAn accepted solution exists. The statement is false.
DISPROVED (LEAN): the site credits Kovač's coloring of the plane in colors with no monochromatic rectangle of area [Ko23]; see the claim page (Kovač, 2023).