Sudoku Solving Techniques

The single most common mistake is reaching for a clever technique when a simple one is still available. Every technique below costs more attention than the one before it, and on a well-formed puzzle the cheap ones keep paying out far longer than people expect.

Pick a digit — say 7 — and look at the three boxes across the top band. For each box, find every row and column that already contains a 7. Those lines are eliminated. If a box has exactly one cell left that no eliminated line passes through, that cell is a 7.

This is cross-hatching, and it is the whole of Sudoku for the first twenty or so digits of an Easy board. Work one digit at a time through all nine boxes before moving to the next digit. Jumping between digits is what makes scanning feel slow — you lose the mental picture of which lines are blocked.

Work the digits you have most of first. If the grid already holds six 5s, the remaining three are heavily constrained and often fall immediately. A digit with only two givens will rarely produce anything and is a waste of a pass.

A naked single is a cell whose candidate list has shrunk to one digit. You are looking at the cell, and the answer is forced. These are easy to spot and easy to trust.

A hidden single is the reverse question. Instead of asking what this cell can be, you ask where this digit can go. If a row has eight cells that cannot take a 4 and one that can, that cell is a 4 — even if it still shows five candidates of its own.

Hidden singles are where almost every stuck board unsticks. They are hard to see precisely because the cell does not look finished: it is carrying other candidates, so the eye passes over it. When you are stuck, go unit by unit — nine rows, nine columns, nine boxes — and for each one, name the digits still missing and count their possible homes.

Put beside each other, the difference is which end of the question you start from. A naked single means looking at a cell and finding one candidate left: quick to spot, quick to trust, and it dries up fast once a board drops below thirty clues. A hidden single means looking at a unit and finding one home left for a digit: easy to miss, because the cell still looks unfinished, and it keeps producing digits deep into Hard long after naked singles have stopped.

From Hard down, you will reach positions where no single exists. The next family of techniques does not place a digit at all — it removes candidates, which then creates a single somewhere else. This is the shift that makes harder Sudoku feel different: you stop looking for answers and start looking for eliminations.

A naked pair is two cells in the same unit holding the same two candidates and nothing else. Between them they will use up both digits, so those two digits can be struck from every other cell in that unit. The pair itself stays unresolved — that is fine. The value is in what it clears.

A hidden pair is two digits that can only live in two cells of a unit. Those cells may be carrying four or five candidates each, but every candidate other than the pair can be deleted from them.

A pointing pair is the most useful of the three and the one worth learning by name. If, within a box, a digit can only go in cells that all share a row, then that digit occupies that row inside this box — so it can be removed from that row everywhere else on the grid. It is the only technique here that reaches outside the unit you are looking at.

Pick a digit. Find two rows in which that digit has exactly two possible cells. If those cells fall in the same pair of columns, you have an X-Wing — four cells at the corners of a rectangle.

Whichever way the digit resolves, it will occupy one corner in each row, and therefore one cell in each of those two columns. So the digit can be eliminated from every other cell in both columns. The same works with rows and columns swapped.

X-Wing has a reputation as the point where Sudoku becomes advanced, and it is genuinely the first technique that requires looking at the whole grid rather than one unit. But it is also rarer than its reputation suggests. On this site it becomes necessary at Expert and occasionally at Hard. If you are reaching for it on Medium, there is a hidden single you have missed.

Difficulty here is set by how many digits the puzzle starts with, and each band corresponds fairly closely to the hardest technique you will need.

• Easy — 36 to 40 clues. Cross-hatching and naked singles. You should not need to write a candidate.
• Medium — 30 to 35 clues. Hidden singles become essential. Still solvable without full notation if you are patient.
• Hard — 25 to 29 clues. Naked and hidden pairs, pointing pairs. Write your candidates; you will not hold it all in your head.
• Expert — 22 to 24 clues. Everything above, plus X-Wing on some boards. Expect long stretches of elimination between placed digits.

For context, the proven minimum for a Sudoku with a unique solution is 17 clues — established by exhaustive computer search in 2012, which also proved no 16-clue puzzle exists. Expert at 22 to 24 is demanding without being one of those extreme constructions.

The timer on this site starts when you fill your first cell, not when the page loads, so there is no cost to reading the board first. Spend that time well: a thirty-second scan that tells you which digits are nearly complete will save minutes later.

Most lost time is not spent thinking, it is spent re-scanning ground you have already covered because you did not record the result. When a unit yields nothing, note that. When you place a digit, immediately check the three units it belongs to for a knock-on single, because one placement very often unlocks another.

And resist the urge to guess when you are one cell from finishing. A wrong digit late in a grid is expensive: it will not contradict anything for several moves, and by the time it does you will have built on it.