challenges / sphere-packing-sphere-radii-n
Spheres with radii i in a sphere
Place n spheres in the unit ball (radius 1) as large as possible (r_i = i · s). Scored against the best-known Packomania records; anything above 1.0 on an n is a new record candidate.
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# Spheres with radii i in a sphere
## Goal
`pack.py` exposes `pack(n: int, time_budget: float, seed: int) -> list[tuple[float, ...]]`: the
centres of `n` spheres inside the unit ball (radius 1) (3 coordinates each). Object `i` (1-based) has radius `(i · s)`, where the eval derives the largest feasible scale `s`; the score is the largest object's radius.
You do not return a radius; the eval derives the largest feasible one from your centres, so there
is nothing to fudge. Make it as large as possible for every `n` you are handed.
## Metric
The eval runs your `pack` on a fixed set of values, `n = 5, 8, 12, 16, 20, 25, 30, 40, 50, 60`, each with the given time
budget (12 s by default), validates the result, and reports
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