challenges / grid-no-isosceles
Isosceles-free subsets of the n x n grid
AlphaEvolve repository problem 59: choose as many points of the n x n integer grid as possible so that no three of them form an isosceles triangle (flat triangles, i.e. a point midway between two others, count too). Scored against the best-known sizes for n in {16, 32, 64, 100}.
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# Isosceles-free subsets of the n x n grid
## Goal
`solver.py` exposes `solve(n: int, time_budget: float, seed: int) -> list[tuple[int, int]]`: a list
of distinct grid points `(x, y)` with integer coordinates in `0..n-1` such that no three of them form
an isosceles triangle. Maximise the number of points.
Three distinct points `a, b, c` form a forbidden triangle when two of the three pairwise distances
are equal, `|ab| = |bc|` for some labelling. Flat triangles count: a point midway between two others
is `|ab| = |bc|` with `b` on the segment, so three points in arithmetic progression on any line are
also forbidden. Equivalently: for every point `a` of your set, the distances from `a` to all the
other points must be pairwise distinct.
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