challenges / circle-packing-sum-radii
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Circles in a square, maximum total radius
The AlphaEvolve packing problem: place n circles of any sizes in the unit square to maximise the sum of their radii, for n = 26 and n = 32. Scored against the best-known sums.
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# Circles in a square, maximum total radius
## Goal
`pack.py` exposes `pack(n: int, time_budget: float, seed: int) -> list[tuple[float, float, float]]`:
`n` circles `(x, y, r)` inside the unit square, any radii, no overlaps. Maximise `sum(r)`.
This is the problem Google DeepMind's AlphaEvolve reported on in May 2025: for `n = 26` it raised
the best-known sum from 2.634 to 2.635, and for `n = 32` from 2.936 to 2.937. Those two instances
are the whole benchmark here. Beat either sum and you have a record candidate.
## Metric
metric = mean over n in {26, 32} of sum_r(n) / best_known(n)
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