Every solvable sudoku yields to the same loop: find what is forced, write it in, and let each placement force the next. This guide turns that loop into a concrete order of operations you can apply to any grid — from the first glance at the givens to the last digit. It assumes you know the board and its single rule; if not, start with how to play sudoku and come back. Nothing below requires guessing, and no step requires holding more than one idea in your head at a time.
Before you write anything: read the grid
Thirty seconds of looking saves ten minutes of wandering. Notice which digits appear most often among the givens — a digit already placed six or seven times is close to finished, and finishing it is usually easy. Notice which rows, columns and boxes are most crowded, because crowded regions are where the first deductions live. A puzzle is solved from its strong points outward, not left to right.
Step 1: sweep for naked singles
A naked single is a cell with only one possible digit left once you account for its row, column and box. Sweep the grid for cells sitting at busy intersections — a cell whose row holds five digits and whose column holds four more can often take only one value. Write each one in as you find it, and check its neighbourhood again before moving on: one placement regularly creates the next. The full anatomy of this deduction is in naked and hidden singles.
Step 2: cross-hatch each digit for hidden singles
Now hunt by digit instead of by cell. Pick a digit with six or more copies placed, and for each box that lacks it, mentally strike out the rows and columns where that digit already stands. If only one cell in the box survives, the digit belongs there — that is a hidden single, and cross-hatching is the fastest way to find one. Work through the heavy digits first, then the lighter ones. On easy puzzles, steps 1 and 2 alone will carry you to the end.
Step 3: when progress stalls, add pencil marks
The moment neither sweep produces a placement, stop scanning harder and start writing smaller. Go region by region and note the candidates — the digits each empty cell could still legally take. Be systematic: marks you only half-trust are worse than none, because every later deduction leans on them. On paper, small corner digits work; online, use the notes mode. The point of marks is not to record confusion but to make the invisible deductions visible.
Step 4: prune candidates with pairs and pointing
With marks in place, the grid starts confessing. Look for a naked pair: two cells in one region sharing the same two candidates, which between them claim both digits and erase those candidates from every other cell in the region. Look for pointing: when all of a box’s candidates for a digit sit in one row or column, that digit must land there, so it disappears from the rest of that row or column outside the box. Each erasure is small, but erasures compound — and sooner or later some cell drops to a single candidate, handing you a placement and restarting the loop.
Step 5: repeat the loop until the grid closes
The whole method is a cycle: place what is forced, re-sweep the neighbourhood of every new digit, and when placements dry up, refine the pencil marks and prune again. Late in a puzzle the grid usually collapses — the last fifteen cells often take less time than the middle fifteen. If a hard grid resists even after honest pruning, the heavier patterns take over: the X-wing and its relatives, catalogued in the sudoku techniques overview, exist precisely for the point where singles and pairs go quiet.
If you think the puzzle is broken
It almost never is. When a contradiction appears — a cell with no candidates, or a digit twice in one row — the honest fix is to find the wrong placement, not to erase everything. Check your most recent entries against their row, column and box, and check the pencil marks that justified them. The most common error is a stale mark: a candidate that should have been erased two moves ago and quietly misled everything after it. This is why tidy marks matter more than fast ones.
Where to practice the method
The loop becomes automatic only through repetition. A gentle grid from the easy sudoku collection lets you drill steps 1 and 2 until they take seconds; the daily sudoku adds one fresh board a day at a steady difficulty; and when pencil-mark discipline feels natural, the hard sudoku shelf will test every step of the chain, pruning included.
Frequently asked questions
Can every sudoku be solved without guessing?
Every properly constructed sudoku — one with a unique solution — can be solved by logic alone. Some very hard grids need advanced patterns rather than just singles and pairs, but needing a stronger deduction is not the same as needing a guess.
What should I look for first in a sudoku?
The most-placed digits and the most crowded regions. Both point at the easiest deductions: naked singles at busy intersections and hidden singles found by cross-hatching the nearly finished digits.
When should I start using pencil marks?
The moment scanning stops producing placements. On easy puzzles that moment may never come; on medium and hard grids, writing candidates early and keeping them tidy is what makes the later steps possible.
How long should one sudoku take to solve?
It depends on the grid, not on you. An easy puzzle commonly falls in a few minutes with steps 1 and 2; a hard one can honestly take half an hour or more, because the pruning loop simply has more work to do.
