Find a 22-by-22 coloring without a monochromatic L

Construct a 3-coloring of the 22 × 22 integer grid with no monochromatic L, if such a coloring exists, potentially using SAT solvers or artificial-intelligence/machine-learning techniques.

Background

The authors report computational success in finding 20 × 20 grids with no monochromatic L, but their attempts to resolve the 21 × 21 case had not produced satisfiability or unsatisfiability. They further speculate that a 22 × 22 example may exist and propose SAT-solving or AI/ML methods as possible tools for finding it. The problem is therefore an explicitly unresolved computational existence question.

References

Though not found, we speculate that a 3-coloring of [22] × [22] with no monochromatic L exists. Try to find one, perhaps by using SAT solvers or AI/ML techniques.

— Ramsey Theory on the Integer Grid: The "L" Problem  (2502.05162 - Mammel et al., 7 Feb 2025) in Section 4, p. 19