Sudoku — Free Online Puzzle Game

Every Sudoku puzzle on this page has exactly one solution. The generator fills a complete valid grid with a seeded backtracking solver, then removes cells one at a time, restoring any that would create a second solution, until the target clue count is reached. Easy keeps 46 givens; Expert strips the grid down to 24, which is close to the minimum that still guarantees uniqueness.

The lead puzzle loads straight away so you can play without clicking New Game first. Its opening row reads 5 3 · · 7 · · · ·, and filling in cell R1C3 with 4 is the first naked single: the row already holds 5 and 3, the top-left box already holds 5, 3, 6, 9, 8, and only 4 fits.

Getting Started: Step by Step

1. Click any empty cell (or use the arrow keys to navigate), then press a digit on your keyboard or tap a number in the numpad row below the board.
2. Conflicting digits turn red immediately. Any cell sharing a row, column or 3x3 box with the same number is flagged, and the error counter in the header increments.
3. Toggle Notes ON (or press N) to switch into pencil-mark mode. The same digit keys fill tiny candidates inside the cell instead of placing a final value. Placing a digit later clears that number from the notes in all peer cells automatically.
4. Press Hint when stuck. The engine searches for a naked single first, then falls back to the precomputed solution grid. The light-bulb counter records how many hints you have used.
5. The timer stops and a trophy banner appears the moment every cell is correctly filled. Press New Game to generate a fresh puzzle at the same or a different difficulty.

How the Algorithm Picks a Move

The hint button uses a two-pass method. Pass one scans every empty cell and collects legal candidates (digits not already present in the row, column, or box). Any cell with exactly one candidate is a naked single and gets filled first. If no naked single exists, pass two looks up the precomputed solution and suggests a cell where the correct digit is still valid. That second pass fires only when human techniques would require looking further ahead than naked and hidden singles.

Precision and Limits by Difficulty

• Easy (46 givens) — Most empty cells have a naked single nearby; no complex chaining is required.
• Medium (36 givens) — Hidden singles appear regularly: a digit that can only go in one cell within a row, column or box.
• Hard (28 givens) — Naked pairs and pointing pairs are needed to make steady progress without guessing.
• Expert (24 givens) — Near the theoretical minimum for a unique-solution grid. X-wings and chains are required; Hint reaches for the solution reference on most moves.
• Uniqueness verification (counting solutions up to 2) is the most expensive step. Expert puzzles can take up to 2 seconds to generate on a slow device; the board appears as soon as it is ready.