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Generator examples

Requests in the generator spec language, each with the puzzle it produced, its card and how long the run took on one core of a desktop machine. The seed fixes the result: the same request on the same version gives the same puzzle. A run that searches for the most of something, or the hardest or easiest puzzle, always uses its whole limits.time and returns the best it found. The times include grading the result in full, which for a hard variant can take longer than the search itself. Written by tools/gen_generator_examples.py; the request files are in docs/examples/specs/.

Curiosities​

Each shows another side of the spec.

As many 10-cages as fit​

Shows a cage sum and the count "max": the run uses its whole time and keeps the result with the most cages.

{"board": {"rows": 9, "cols": 9},
 "digits": 9,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [3, 3]},
  {"type": "cage", "sum": 10, "count": "max"}],
 "quality": {},
 "limits": {"time": 300, "seed": 1}}

24 cages, 1 given. Very Hard, difficulty 13.1, about 59.0 min. Contains: Hidden Single, Naked Single, Pointing / Box-Line Reduction, Killer cage combinations, Hidden Pair, Naked Quad, Innies & outies as a virtual cage, Innies & outies over several houses, Two rules together, Band set theory with cages. Generated in 426 s, the best of 5 found (time limit 300 s); the publishing checks refused 2 other candidates (unusual).

One whisper, 25 cells or more​

Shows a line length with no upper bound, and 180° symmetry of the givens.

{"board": {"rows": 9, "cols": 9},
 "digits": 9,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [3, 3]},
  {"type": "line", "kind": "whisper", "length": [25, null], "count": 1}],
 "symmetry": [{"kind": "rot180", "of": "givens"}],
 "quality": {},
 "limits": {"time": 300, "seed": 1}}

1 whisper, 12 givens. Very Easy, difficulty 5.2, about 13.2 min. Contains: Hidden Single, Line / dot read without notes. Generated in 32 s, 7 attempts (time limit 300 s).

Long whispers and renbans​

Shows lengths on two templates at once: whispers of 7 cells or more, renbans of at least 5 ("auto": as many as needed).

{"board": {"rows": 9, "cols": 9},
 "digits": 9,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [3, 3]},
  {"type": "line", "kind": "whisper", "length": [7, null], "count": 2},
  {"type": "line", "kind": "renban", "length": [5, null], "count": "auto"}],
 "quality": {},
 "limits": {"time": 600, "seed": 1}}

6 renbans, 2 whispers, 6 givens. Medium, difficulty 11.2, about 41.2 min. Contains: Hidden Single, Line / dot read without notes, Last cell of a cage / line, Naked Single, Pointing / Box-Line Reduction, Line ranges (thermo / whisper bounds), Digit counting, Two rules together. Generated in 520 s, 5 attempts (time limit 600 s).

Three tall thermometers​

Shows an exact count with a length range: three thermos of 7 to 9 cells.

{"board": {"rows": 9, "cols": 9},
 "digits": 9,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [3, 3]},
  {"type": "line", "kind": "thermo", "length": [7, 9], "count": 3}],
 "quality": {},
 "limits": {"time": 180, "seed": 1}}

3 thermos, 13 givens. Easy, difficulty 5.0, about 12.0 min. Contains: Hidden Single, Line / dot read without notes, Naked Single. Generated in 61 s, 5 attempts (time limit 180 s).

The gentlest X-Wing​

Shows difficulty "min" with a required technique: the easiest puzzle found in the time that still needs an X-Wing.

{"board": {"rows": 9, "cols": 9},
 "digits": 9,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [3, 3]}],
 "where": {"difficulty": "min", "contains": {"codes": ["XWG"], "strict": true}},
 "quality": {},
 "limits": {"time": 300, "seed": 1}}

24 givens. Hard, difficulty 5.3, about 10.6 min. Contains: Hidden Single, Naked Single, X-Wing. Generated in 300 s, the best of 17 found (time limit 300 s); the publishing checks refused 1 other candidates (unusual).

The hardest 0-clue 6×6 kropki​

Shows difficulty "max": no givens, a minimal set of dots (count "min"), the hardest found in the time.

{"board": {"rows": 6, "cols": 6},
 "digits": 6,
 "givens": {"count": 0},
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [2, 3]},
  {"type": "edge", "kind": "kropki", "count": "min"}],
 "where": {"difficulty": "max"},
 "quality": {},
 "limits": {"time": 600, "seed": 5}}

11 white dots, 1 black dot, 0 givens. Expert, difficulty 14.4, about 24.5 min. Contains: Hidden Single, Clue Facts, Pointing / Box-Line Reduction, Pair rules (dots, whispers, anti-knight...), Line ranges (thermo / whisper bounds), Naked Pair, Two rules together, 2-String Kite, Band set theory with cages, Case analysis. Generated in 602 s, the best of 61 found (time limit 600 s).

Every even cell shaded​

Shows the count "max" on a cell template: every even cell is marked, and the run keeps the result with the fewest givens.

{"board": {"rows": 9, "cols": 9},
 "digits": 9,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [3, 3]},
  {"type": "cell", "kind": "even", "count": "max"}],
 "quality": {},
 "limits": {"time": 300, "seed": 1}}

36 even cells, 10 givens. Hard, difficulty 7.7, about 22.9 min. Contains: Hidden Single, Pointing / Box-Line Reduction, Pair / triple in the head, Hidden Pair, Hidden Quad, X-Wing, Skyscraper (in the head), Simple Colouring. Generated in 300 s, the best of 211 found (time limit 300 s); the publishing checks refused 27 other candidates (unusual).

Only X, no V​

Shows an exact count of 0 forbids a letter: as many X clues as fit and no V.

{"board": {"rows": 9, "cols": 9},
 "digits": 9,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [3, 3]},
  {"type": "edge", "kind": "xv", "letter": "X", "count": "max"},
  {"type": "edge", "kind": "xv", "letter": "V", "count": 0}],
 "quality": {},
 "limits": {"time": 300, "seed": 1}}

24 Xs, 9 givens. Medium, difficulty 8.7, about 29.6 min. Contains: Hidden Single, Line / dot read without notes, Clue Facts, Naked Single, Pointing / Box-Line Reduction, Pair rules (dots, whispers, anti-knight...), Hidden Pair, Two rules together. Generated in 302 s, the best of 27 found (time limit 300 s); the publishing checks refused 12 other candidates (barely_used, barely_used/unusual, unusual).

A 6×6 killer tiled by cages​

Shows the count "tile": cages cover the whole board.

{"board": {"rows": 6, "cols": 6},
 "digits": 6,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [2, 3]},
  {"type": "cage", "count": "tile"}],
 "quality": {},
 "limits": {"time": 180, "seed": 1}}

10 cages, 0 givens. Easy, difficulty 5.3, about 9.3 min. Contains: Hidden Single, Naked Single, Pointing / Box-Line Reduction, Notes in the head, Killer cage combinations. Generated in 2 s, 5 attempts (time limit 180 s).

A 4×4 with quarter-turn symmetry​

Shows the smallest board; 90° symmetry (it needs square boxes).

{"board": {"rows": 4, "cols": 4},
 "digits": 4,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [2, 2]}],
 "symmetry": [{"kind": "rot90", "of": "givens"}],
 "quality": {},
 "limits": {"time": 180, "seed": 1}}

4 givens. Very Easy, difficulty 0.1, about 0.7 min. Contains: Hidden Single. Generated in 0 s, 1 attempt (time limit 180 s).

An 8×8 with at most six dots​

Shows an 8×8 board and the element cap (where.elements).

{"board": {"rows": 8, "cols": 8},
 "digits": 8,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [2, 4]},
  {"type": "edge", "kind": "kropki", "count": "auto"}],
 "where": {"elements": {"max": 6}},
 "quality": {},
 "limits": {"time": 180, "seed": 1}}

5 white dots, 1 black dot, 13 givens. Expert, difficulty 12.7, about 35.6 min. Contains: Hidden Single, Naked Single, Pointing / Box-Line Reduction, Pair rules (dots, whispers, anti-knight...), Two rules together, Band set theory with cages, Alternating Inference Chain. Generated in 29 s, 2 attempts (time limit 180 s); the publishing checks refused 1 other candidates (barely_used).

Larger requests​

Multi-grid layouts, a request is a puzzle file with blanks: one box_grid rule per grid (the origins of a named layout: samurai, super-samurai, twodoku, butterfly, ...), locked rules every result carries (diagonals, extra regions, windoku windows, anti-knight, anti-king: rules of different digits), and givens per grid (givens.grids, the grids in reading order of their origins). Then requests kept as files in docs/examples/specs/; run one with pencilmark generate FILE.

A super samurai: a variant per row, harder to the right​

Shows eight overlapping grids (box_grid rules at the super-samurai origins), locked rules per row of grids (X diagonals on top, windoku windows in the middle, an asterisk at the bottom) and a given floor per grid (givens.grids) that thins out from left to right.

{"board": {"rows": 21, "cols": 33},
 "digits": 9,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [3, 3]},
  {"type": "box_grid", "origin": "r1c13", "box": [3, 3]},
  {"type": "box_grid", "origin": "r1c25", "box": [3, 3]},
  {"type": "box_grid", "origin": "r7c7", "box": [3, 3]},
  {"type": "box_grid", "origin": "r7c19", "box": [3, 3]},
  {"type": "box_grid", "origin": "r13c1", "box": [3, 3]},
  {"type": "box_grid", "origin": "r13c13", "box": [3, 3]},
  {"type": "box_grid", "origin": "r13c25", "box": [3, 3]},
  {"type": "region", "kind": "diagonal", "cells": ["r1c1", "r2c2", "r3c3", "r4c4", "r5c5", "r6c6", "r7c7", "r8c8", "r9c9"]},
  {"type": "region", "kind": "diagonal", "cells": ["r1c9", "r2c8", "r3c7", "r4c6", "r5c5", "r6c4", "r7c3", "r8c2", "r9c1"]},
  {"type": "region", "kind": "diagonal", "cells": ["r1c13", "r2c14", "r3c15", "r4c16", "r5c17", "r6c18", "r7c19", "r8c20", "r9c21"]},
  {"type": "region", "kind": "diagonal", "cells": ["r1c21", "r2c20", "r3c19", "r4c18", "r5c17", "r6c16", "r7c15", "r8c14", "r9c13"]},
  {"type": "region", "kind": "diagonal", "cells": ["r1c25", "r2c26", "r3c27", "r4c28", "r5c29", "r6c30", "r7c31", "r8c32", "r9c33"]},
  {"type": "region", "kind": "diagonal", "cells": ["r1c33", "r2c32", "r3c31", "r4c30", "r5c29", "r6c28", "r7c27", "r8c26", "r9c25"]},
  {"type": "region", "kind": "window", "cells": ["r8c8", "r8c9", "r8c10", "r9c8", "r9c9", "r9c10", "r10c8", "r10c9", "r10c10"]},
  {"type": "region", "kind": "window", "cells": ["r8c12", "r8c13", "r8c14", "r9c12", "r9c13", "r9c14", "r10c12", "r10c13", "r10c14"]},
  {"type": "region", "kind": "window", "cells": ["r12c8", "r12c9", "r12c10", "r13c8", "r13c9", "r13c10", "r14c8", "r14c9", "r14c10"]},
  {"type": "region", "kind": "window", "cells": ["r12c12", "r12c13", "r12c14", "r13c12", "r13c13", "r13c14", "r14c12", "r14c13", "r14c14"]},
  {"type": "region", "kind": "window", "cells": ["r8c20", "r8c21", "r8c22", "r9c20", "r9c21", "r9c22", "r10c20", "r10c21", "r10c22"]},
  {"type": "region", "kind": "window", "cells": ["r8c24", "r8c25", "r8c26", "r9c24", "r9c25", "r9c26", "r10c24", "r10c25", "r10c26"]},
  {"type": "region", "kind": "window", "cells": ["r12c20", "r12c21", "r12c22", "r13c20", "r13c21", "r13c22", "r14c20", "r14c21", "r14c22"]},
  {"type": "region", "kind": "window", "cells": ["r12c24", "r12c25", "r12c26", "r13c24", "r13c25", "r13c26", "r14c24", "r14c25", "r14c26"]},
  {"type": "region", "kind": "extra", "cells": ["r14c5", "r15c2", "r15c8", "r17c1", "r17c5", "r17c9", "r19c2", "r19c8", "r20c5"]},
  {"type": "region", "kind": "extra", "cells": ["r14c17", "r15c14", "r15c20", "r17c13", "r17c17", "r17c21", "r19c14", "r19c20", "r20c17"]},
  {"type": "region", "kind": "extra", "cells": ["r14c29", "r15c26", "r15c32", "r17c25", "r17c29", "r17c33", "r19c26", "r19c32", "r20c29"]}],
 "givens": {"grids": [[38, null], [27, null], [0, null], [32, null], [23, null], [38, null], [27, null], [0, null]]},
 "quality": {},
 "limits": {"time": 3600, "seed": 1}}

193 givens. Hard, difficulty 4.4, about 71.6 min. Contains: Hidden Single, Pointing / Box-Line Reduction, Pair / triple in the head, Naked Pair, Equal cells (same digit), Skyscraper, Turbot Fish, Simple Colouring, Short chain in the head. Generated in 284 s, 10 attempts (time limit 3600 s); the publishing checks refused 9 other candidates (unusual).

A samurai​

Shows a named layout: five grids sharing their corner boxes, 180° symmetry of the givens.

{"board": {"rows": 21, "cols": 21},
 "digits": 9,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [3, 3]},
  {"type": "box_grid", "origin": "r1c13", "box": [3, 3]},
  {"type": "box_grid", "origin": "r7c7", "box": [3, 3]},
  {"type": "box_grid", "origin": "r13c1", "box": [3, 3]},
  {"type": "box_grid", "origin": "r13c13", "box": [3, 3]}],
 "symmetry": [{"kind": "rot180", "of": "givens"}],
 "quality": {},
 "limits": {"time": 1800, "seed": 1}}

108 givens. Hard, difficulty 4.6, about 46.8 min. Contains: Hidden Single, Pointing / Box-Line Reduction, Skyscraper (in the head). Generated in 3 s, 1 attempt (time limit 1800 s).

Twodoku, Hard​

Shows two grids sharing a box, with a band target.

{"board": {"rows": 15, "cols": 15},
 "digits": 9,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [3, 3]},
  {"type": "box_grid", "origin": "r7c7", "box": [3, 3]}],
 "where": {"band": "Hard"},
 "quality": {},
 "limits": {"time": 900, "seed": 1}}

39 givens. Hard, difficulty 6.3, about 21.7 min. Contains: Hidden Single, Naked Single, Pointing / Box-Line Reduction, Hidden Pair, Skyscraper. Generated in 1 s, 1 attempt (time limit 900 s).

A butterfly killer​

Shows four grids overlapping on a 12 × 12 board, with cages.

{"board": {"rows": 12, "cols": 12},
 "digits": 9,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [3, 3]},
  {"type": "box_grid", "origin": "r1c4", "box": [3, 3]},
  {"type": "box_grid", "origin": "r4c1", "box": [3, 3]},
  {"type": "box_grid", "origin": "r4c4", "box": [3, 3]},
  {"type": "cage", "count": [6, null]}],
 "quality": {},
 "limits": {"time": 1800, "seed": 1}}

18 cages, 2 givens. Medium, difficulty 7.9, about 57.6 min. Contains: Hidden Single, Naked Single, Pointing / Box-Line Reduction, Notes in the head, Killer cage combinations, Equal cells (same digit). Generated in 220 s, 2 attempts (time limit 1800 s); the publishing checks refused 1 other candidates (barely_used).

Killer with German whispers and two givens​

Cages and whisper lines, exactly two givens, Hard.

{"board": {"rows": 9, "cols": 9},
 "digits": 9,
 "givens": {"count": 2},
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [3, 3]},
  {"type": "cage", "count": [1, null]},
  {"type": "line", "kind": "whisper", "count": [1, null], "value": 5}],
 "where": {"band": "Hard"},
 "quality": {},
 "limits": {"results": 1, "time": 900, "seed": 3},
 "fields": ["difficulty", "band", "contains", "issues"]}

8 cages, 7 whispers, 2 givens. Hard, difficulty 9.6. Contains: Hidden Single, Line / dot read without notes, Last cell of a cage / line, Clue Facts, Naked Single, Pair / triple in the head, Pair rules (dots, whispers, anti-knight...), Naked Pair, Skyscraper (in the head). Generated in 449 s, 16 attempts (time limit 900 s); the publishing checks refused 1 other candidates (unusual).

A 0-clue 6×6 kropki​

No givens, a minimal set of kropki dots, difficulty at least 3.

{"board": {"rows": 6, "cols": 6},
 "digits": 6,
 "givens": {"count": 0},
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [2, 3]},
  {"type": "edge", "kind": "kropki", "count": "min"}],
 "where": {"difficulty": [3, 99]},
 "quality": {},
 "limits": {"time": 600, "seed": 5}}

8 white dots, 3 black dots, 0 givens. Expert, difficulty 13.3, about 26.9 min. Contains: Hidden Single, Clue Facts, Pointing / Box-Line Reduction, Pair rules (dots, whispers, anti-knight...), Line ranges (thermo / whisper bounds), Naked Pair, Hidden Pair, Two rules together, Simple Colouring, Band set theory with cages, Alternating Inference Chain, Case analysis. Generated in 15 s, 1 attempt (time limit 600 s).

Nine variants on one 9×9​

At least one cage, thermo, whisper, renban, between line, arrow, kropki dot, XV clue and odd / even cell, each needed by the solve.

{"board": {"rows": 9, "cols": 9},
 "digits": 9,
 "rules": [{"type": "box_grid", "origin": "r1c1", "box": [3, 3]},
  {"type": "cage", "count": [1, null]},
  {"type": "line", "kind": "thermo", "count": [1, null]},
  {"type": "line", "kind": "whisper", "count": [1, null]},
  {"type": "line", "kind": "renban", "count": [1, null]},
  {"type": "line", "kind": "between", "count": [1, null]},
  {"type": "arrow", "count": [1, null]},
  {"type": "edge", "kind": "kropki", "count": [1, null]},
  {"type": "edge", "kind": "xv", "count": [1, null]},
  {"type": "cell", "kind": "parity", "count": [1, null]}],
 "where": {"elements": {"max": 20}},
 "quality": {},
 "limits": {"time": 1800, "seed": 9}}

5 thermos, 3 renbans, 2 Xs, 1 arrow, 1 between line, 1 cage, 1 white dot, 1 odd cell, 1 V, 1 whisper, 1 given. Expert, difficulty 14.4, about 67.5 min. Contains: Hidden Single, Line / dot read without notes, Clue Facts, Naked Single, Pointing / Box-Line Reduction, Notes in the head, Arrow sums, Pair rules (dots, whispers, anti-knight...), Line ranges (thermo / whisper bounds), Naked Pair, Hidden Pair, Naked Quad, Two rules together, Domino pairs (dots / XV), Band set theory with cages, Case analysis. Generated in 496 s, 2 attempts (time limit 1800 s); the publishing checks refused 1 other candidates (unusual).

Not possible yet​

docs/examples/specs/reserved/ holds requests that use parts reserved for later versions of the spec (Generator spec, section 7); the generator refuses them today: a classic with exactly one X-Wing, givens in the shape of a heart and a displaced jigsaw. A 16×16 killer with exactly 32 cages and no givens is also out of reach: the uniqueness search does not finish.