How to solve a sudoku

The rule

Fill the grid with the digits 1 to 9, each one appearing exactly once per row, per column, and per 3×3 box. A well-built puzzle always has a single unique solution, one you can reach without ever guessing.

Step 1 — sweep digit by digit

Pick a digit, say 7. Go through each box one at a time: if it's still missing, look for the one cell it can go in, since every other cell in that box is already ruled out by its row or column. That's a hidden single: 7 might look like a fit for several cells in the box if you checked them one by one, but only one of them escapes every row and column that already has a 7. Start with the digits you've placed the most of — they rule out the most cells, so the first hidden singles fall fast.

Step 2 — cell by cell

Now flip your approach. Instead of tracking one digit across the whole grid, look at one empty cell at a time: if every digit but one is already taken on its row, column, or box, that last one has to go there. That's a naked single, the most straightforward deduction in the game — no need to check the neighbouring cells, it solves itself.

Step 3 — pencil in the candidates

Once steps 1 and 2 stop turning anything up, it's time to pencil in the candidates: for every empty cell, the digits that are still possible given what's already on the board. Two quick ways to do this without burning your whole game on it: write them in yourself with the Note tool, or switch on Candidates in Solvissima to have them show up automatically across the grid. Every technique from here on works on these candidates rather than on placed digits — each one strips away a few, until a cell or a digit is left with only one option.

Step 4 — eliminate with techniques

Pencilling in candidates doesn't always reveal a single straight away. When that happens, eliminate candidates with techniques, roughly in the order they come up most often:

• Pointing pairs and claiming pairs (reduction) — a digit confined to a single row or column within a box can be ruled out of the rest of that row or column.
• Naked pairs and naked triples — two or three cells that share exactly the same candidates.
• Hidden pairs — two digits confined to the same two cells of a zone.
• For Hard puzzles and beyond: X-Wing, XY-Wing, and the fish patterns Swordfish and Jellyfish.

Step 5 — never guess

A well-built puzzle always solves by deduction, step after step, right down to the last cell. If you get stuck, it means a technique is still eluding you — not that it's time to try your luck. The Hypothesis tool lets you test a lead you're not sure about: place it, keep solving as if it were true, and cancel it with one click if it runs into a wall. It's not a coin flip, more like a cell you test cleanly, always knowing you can step back without losing your progress.

Mistakes that cost you time

• Guessing a digit without being sure, then having to unwind it several cells later.
• Forgetting to strike out a candidate after placing a digit, so the grid looks stuck for no reason.
• Jumping to an advanced technique before pencilling in candidates, on a grid that isn't ready for it yet.

Recap

1. Sweep each digit, box by box: look for the hidden single.
2. Check each cell: if only one digit is left possible, place the naked single.
3. Nothing turning up? Pencil in the candidates.
4. Eliminate with techniques, from the most common to the rarest.
5. Never guess: deduce, or test a lead with the Hypothesis tool.

Keep improving

Want to train technique by technique, with a coach that walks through the reasoning with you at every step? Head over to Your next step. To put the method into practice right now, start with an Easy puzzle. To ease into it gently, try 6×6 sudoku.