Sudoku

Fill the grid so every row, column and region holds each digit exactly once.

What it is

A 9×9 grid (4×4 and 6×6 for younger solvers) partly filled with digits. The remaining cells must be completed so that every row, every column, and every marked region contains each digit exactly once. Three variants ship from this crate: classic (rectangular boxes), jigsaw (irregular regions), and killer (boxes plus dashed cages whose distinct digits sum to a printed target — conventionally with no digits given at all).

How to play

Find a cell whose value is forced — a digit that can go nowhere else in its row, column or region — write it in, and repeat. Harder boards need candidate reasoning: mark which digits each empty cell can still take, then eliminate with pairs, triples, box–line interactions and fish patterns. A proper sudoku never requires guessing, and every puzzle from this crate is verified to be solvable by inference alone.

Purpose

The anchor puzzle of any mixed collection — instantly recognised, deeply studied, and with a real difficulty vocabulary (the technique ladder) that most other puzzles lack. It is also the crate that drove the workspace’s shared constraint engine: rows, columns and regions are AllDifferent groups, killer cages reuse the kakuro sum propagator, and jigsaw is just a different partition.

History

The modern form appeared as Number Place in Dell Pencil Puzzles & Word Games (1979), designed by Howard Garns. Nikoli introduced it to Japan in 1984, where the name sūdoku (“the digits must be single”) stuck. Wayne Gould’s computer-generated puzzles in The Times (2004) started the worldwide boom. Killer sudoku descends from Japanese “samunamupure” (sum number place); jigsaw variants circulate as “squiggly” or “irregular” sudoku.

This implementation

• Spec knobs: size (4/6/9), variant (classic/jigsaw/killer), difficulty target, symmetric digging, max_cage (killer).
• Generation: answer first (solver fills a full grid), then dig clues in 180°-symmetric pairs while the board stays solvable by inference at the target band’s technique ceiling. Killer reveals digits only when the cages alone leave the board ambiguous.
• Guarantees: exactly one solution, proven; the printed difficulty is the hardest technique the ladder actually used, never an estimate. Techniques run from singles through pairs, box–line, X-Wing and Swordfish.
• Expert: unreachable by digging (of 600 maximally dug boards, none needed a Swordfish), so Expert boards are climbed into existence — clue swaps that never decrease the measured difficulty, walking the space of unique boards until one needs a Swordfish. Hits on about two seeds in three, in 15–35 s; a miss returns an honest Hard, labelled with the requested band alongside. Classic variant only, and the climb trades the symmetric clue pattern for the fish pattern it hunts.