Settability

For the greeter templates, we introduced the concept of settability, represented by a settability score. This is a weighted metric designed to quantify how easily a crossword grid can be filled with words. It focuses on three primary factors: Openness, Constraint Density, and Average Word Length.

The New Puzzle greeter ships with templates that are sorted by settability, from easiest- to hardest-to-fill. We only apply this score to standard crosswords. In practice cryptic puzzles are much easier to fill, and the overall concept isn’t that useful with those puzzles.

It is calculated in tools/grid-extractors/settability.py

Scoring Formula

The score is a weighted sum of three sub-scores, capped at a maximum of 100.00:

  • Openness (30%): Calculated as the ratio of normal cells to the total grid area. Scores are prioritized for grids with an openness factor above 0.75.

  • Constraint Density (30%): Measures the “tightness” of the grid by comparing the total length of all words to the number of normal cells. It favors grids where words are well-integrated but not overly restricted.

  • Average Word Length (40%): Calculated as the total length of all words divided by the total number of words. The score favors grids with an average word length significantly higher than 3.5 to avoid “choppy” layouts with too many short entries.

Settability Buckets

To simplify UI categorization, scores are mapped to five discrete buckets.

  • Bucket 1: Score ≤ 38 (Most constrained/difficult to set)

  • Bucket 2: Score 39–41

  • Bucket 3: Score 42–47

  • Bucket 4: Score 48–53

  • Bucket 5: Score > 53 (Most open/easiest to set)

Derivation

These values and percents were determined empirically, by looking at a large set of puzzles.