Apaxdor/kakuro_kraze

Kakuro Kraze (v2)

Procedurally generated Kakuro puzzles (grid sizes 9, 11, 15). v2 guarantees every puzzle has exactly one solution, established independently of the generator (see "Validation"). The earlier release (v1, tag v1) labelled puzzles unique using a generator flag that was wrong for puzzles whose solve timed out (4.9 % / 15.7 % / 55.7 % of the 9 / 11 / 15 test sets had two or more solutions).

Each config is one grid size: grid9, grid11, grid15; each has train 50 000 / validation 5 000 / test 5 000.

from datasets import load_dataset
ds = load_dataset("Apaxdor/kakuro_kraze", "grid11")
print(ds["train"][0])

Format

puzzle and solution are strings of one bracketed row per line. Cell codes: 0 black, 1 empty white cell (puzzle only), (right_sum, down_sum) clue cell (0 = no clue in that direction), and in solution white cells hold the digit 1-9. Rules: each run sums to its clue, digits do not repeat within a run.

column	meaning
puzzle, solution	as above
puzzle_id	xxh64 of the solution string
grid_size	9, 11 or 15
num_entry_squares, n_white	number of white cells
n_runs, frac_len1_runs	runs and the share of length-1 runs
solver_prop_fixed_frac	share of white cells fixed by constraint propagation alone (no guessing)
solver_search_nodes	nodes of a propagation + most-constrained-cell backtracking search that exhaustively proves uniqueness (deterministic; 1 = solved by propagation)
difficulty_score, difficulty_tertile	rank-combined solver difficulty and its tertile (0 easy, 2 hard) within the grid size
verified_unique, is_exclusive	always True in v2 (verified independently of the generator, see Validation)
legacy_split, topped_up	whether the puzzle was in a v1 split (and which), or newly added in v2 (topped_up=True)

Validation (v2)

• Every puzzle was solved by (a) OR-Tools CP-SAT counting solutions up to 2, (b) a separate propagation + backtracking solver, and (c) CP-SAT block-and-resolve (forbid the stored solution, require infeasible). All 180 000 puzzles are unique and match the stored solution.
• No exact or canonical duplicates (crop to bounding box + transpose) between or within splits; no near-duplicates at <=10 % cell Hamming distance (MinHash-LSH with exact verification; probabilistic recall).
• Repair policy: v1 puzzles that are independently unique were kept in their original split; the rest were replaced by never-released unique puzzles from the same generator (for 15x15, additionally generated from new seeds). legacy_split / topped_up identify them, so v1 results can be re-scored on the kept subset (test: 4 756 / 4 213 / 2 217 puzzles for 9 / 11 / 15).

Difficulty

difficulty_score is the mean of the percentile ranks of solver_search_nodes and 1 - solver_prop_fixed_frac, ranked within each grid size; difficulty_tertile splits it at the 1/3 and 2/3 quantiles (cut points 0.311/0.669 for grid9, 0.333/0.668 for grid11, 0.344/0.663 for grid15). It measures the effort of one deterministic constraint solver, not human difficulty, and tertiles are relative within a grid size (compare the raw columns across sizes). The solver is deterministic (constraint propagation, then backtracking on the most constrained cell), so the score does not depend on machine load. The v1 generator's difficulty field was removed because it was timeout-capped and machine-load dependent.

Known properties and limitations

• Unique-only filtering changes the distribution: v2 boards are slightly smaller and have more length-1 runs than v1 (15x15 test mean white cells 76.1 -> 72.4; length-1 runs 63.6 % -> 68.1 %). Roughly two thirds of runs are single-cell runs, which makes many cells directly determined.
• Components of up to 2 white cells recur across train and test by necessity; components of 6+ cells essentially never do (about 53 % of test white cells lie in components that also occur in train).
• Generator artifact: in every solution the digits are distinct across each whole row and each whole column (100 % of puzzles), which is stronger than the Kakuro rules (distinctness is only required within a run). A model could exploit this; evaluate on other generators before claiming general Kakuro ability.
• The generator is a single fixed procedure; results on this data do not establish general Kakuro-solving ability on other generators or human puzzles.
• Legacy puzzles: 15x15 v2 test is 56 % new puzzles; 11x11 16 %; 9x9 5 %.

Generator, uniqueness check and cleaning pipeline: https://github.com/data-hound/pykakuro (see the README section on the dataset).