STRATEGY.md

Strategy

Goals

• Find a valid 3x3 magic square of distinct perfect squares, or produce the strongest near misses.
• Compare algorithm variants under a consistent scoring and timing budget.
• Iterate by tweaking promising algorithms based on observed outputs.

Core Scoring (near-miss ranking)

Let the 3x3 entries be integers (not necessarily squares). Compute the 8 line sums and set the target magic sum to the average of those sums.

• Magic-ness error:
  • E_sum = sqrt((1/8) * sum((S_k - M)^2))
• Square-ness error:
  • E_sq = sqrt((1/9) * sum((x - round(sqrt(x))^2)^2))
• Distinctness penalty:
  • E_dist = 9 - count(distinct entries)

Optional normalization (scale-free):

• E_sum_norm = E_sum / max(1, |M|)
• E_sq_norm = E_sq / max(1, median(x))

Combined score (lower is better):

• Score = w1 * E_sum_norm + w2 * E_sq_norm + w3 * E_dist
• Default weights: w1 = 1.0, w2 = 1.0, w3 = 2.0

Experiment Loop

1. Run algorithm variant under a fixed time budget.
2. Record best candidate, score, throughput, and time to first decent near miss.
3. Review the structure of top candidates and tweak parameters or heuristics.
4. Re-run and compare against prior results.

Output Tracking

• Keep a "hall of fame" of best candidates and scores per algorithm variant.
• Log parameter settings and performance for repeatability.

Success Criteria

• Exact hit: all entries are perfect squares, distinct, and all 8 line sums equal.
• Near-miss: minimum score under agreed weights; prioritize low E_sum and zero E_sq, then reduce E_dist.