Rules, pencil marks, and the techniques that solve any grid without guessing
Sudoku is a pure logic puzzle played on a 9x9 grid, subdivided into nine 3x3 boxes. Some cells start filled in - the "givens" - and your job is to complete the rest so that every row, every column, and every 3x3 box contains each digit from 1 to 9 exactly once. There's no arithmetic involved at all; the digits could just as well be nine colors or nine letters. It's a placement puzzle, not a math puzzle.
A properly constructed Sudoku (and every puzzle we generate is one) has exactly one solution, reachable by logic alone. That's the contract of the game: you never have to guess. Everything below is about building the deduction toolkit that makes that promise real, from the scan-and-fill techniques that crack easy grids to the candidate work that hard ones demand.
That single overlap - each cell answering to three units at once - is where all the depth comes from. A digit placed in one cell ripples through 20 other cells' possibilities.
Start every puzzle by scanning: pick a digit that already appears often - say there are six 7s placed - and hunt for the boxes still missing one. Cross-hatching is the mechanical version: for a box missing its 7, mentally draw lines through every row and column that already contains a 7. Those lines eliminate cells in the box, and frequently only one cell survives - that's where the 7 goes. Cycle through digits 1 to 9 this way and easy puzzles half-solve themselves before you write a single pencil mark.
When scanning stalls, switch to candidates: small pencil-mark digits noting every value a cell could still legally hold. Our Sudoku has a built-in pencil-mark mode, so you can annotate without losing track. Good candidate discipline has two halves - writing marks honestly (every legal digit, not just the ones you suspect) and erasing them immediately whenever a placement rules them out. Nearly every advanced technique is really just a pattern you spot in well-maintained pencil marks.
A naked single is a cell whose candidates have dwindled to exactly one digit - the placement is forced, write it in. A hidden single is subtler: a cell may have several candidates, but if it's the only cell in its row, column, or box that can hold a particular digit, that digit must go there regardless of the other candidates. Hidden singles are the workhorse of intermediate play; when you feel stuck, checking each unit for a digit with only one home is the first thing to try.
When two cells in the same unit both have exactly the same two candidates - say both show only 4 and 9 - those two digits are locked into those two cells, even though you don't yet know which goes where. That means you can erase 4 and 9 from every other cell in that unit. Naked pairs don't place a digit directly, but the eliminations they cause routinely create fresh singles elsewhere. The same idea extends to triples, and it's your entry point into the whole family of elimination-based techniques.
Every PlayVersusAI puzzle is freshly generated with a unique solution, and the four levels differ in how much of the toolkit they demand. Easy grids offer plenty of givens and fall entirely to scanning and naked singles - ideal for building speed. Medium removes more givens, so you'll need hidden singles and light pencil-mark work. Hard requires sustained candidate management: expect naked pairs and positions where progress comes only from eliminations. Expert starts with a sparse grid and chains several techniques together before the first easy digit appears. The solve timer tracks your best time per level, and error checking can be toggled on while you're learning and off when you want the pure experience.
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