tammes-30

Metric min-angle-deg, maximize · Best known 38.5971 (Hardin, Sloane & Smith 1994) · Play · Code · All example problems

hillclimb problem get tammes-30      # copies the problem into hillclimb/problems/
hillclimb verify tammes-30           # scores the floor; spread 0, the verifier is exact
hillclimb run tammes-30 --budget 15m

The problem

Place exactly 30 points on the unit sphere so that the smallest angular separation between any two of them is as large as possible (a max-min objective over all C(30,2) = 435 pairs — the "spherical code" or "repelling dictators" problem).

Constraints (verified programmatically):

• exactly 30 rows with finite coordinates
• every row is a non-zero vector; the verifier normalizes each row to unit length, so you may submit any non-zero direction

This is a classic hard continuous optimization problem. The best known value for n = 30 is 38.5971 degrees (Hardin, Sloane & Smith 1994). Latitude rings and lattices are weak. Good approaches: many random or Fibonacci-spiral starts, a steep repulsion surrogate (maximize the softmin of the pairwise angles, or minimize sum 1/d^p with a large p) followed by an exact polish (SLSQP: maximize t subject to every pairwise angle >= t), and restarts that keep the best. numpy and scipy are available.

Submission format

Write submission.csv in the working directory with the header id,x,y,z and 30 rows (id = 0..29), like sample_submission.csv (a weak valid baseline: points on a few latitude rings).

Scoring

The orchestrator runs problem/verify.py after your script finishes. The verifier normalizes the rows, computes the minimum pairwise angle in degrees and prints val_score: <min angle> (0.0 if invalid). Higher is better.

There is no train/test data; this is a pure optimization problem. Keep total runtime well within the execution time limit.