From your first single to the XY-Wing
Every fairly constructed Sudoku can be solved without guessing. When you get stuck, what is missing is usually not luck but the right technique. This page walks you through eight solving strategies in ascending difficulty: from the two singles that crack any easy puzzle to X-Wing, Swordfish and XY-Wing for the expert level. Each one is explained so you can apply it in your very next game.
A Naked Single is a cell where only one number remains possible. Check which of the nine digits already appear in the cell's row, column and 3x3 box. If eight are taken, the ninth is forced. It sounds trivial, yet it is the most common solving technique there is: in an easy puzzle with around 40 clues, more than half of all cells can often be filled with singles alone. Look for cells whose row, column and box together already contain many numbers.
The Hidden Single reverses the perspective. Instead of asking which numbers fit into a cell, you ask where a specific number can still go within a unit. If a block is missing its 7 and eight of the nine cells are blocked by a row or column, the 7 must go into the last free cell. That cell may well hold several candidates, hence the name. Together with the Naked Single, this technique is enough for all easy and most medium puzzles.
When a number is only possible in a single row within a box, it must occupy that row inside the box. It follows that you can remove the number as a candidate from the same row outside the box. The same logic applies to columns. This technique, also called a Pointing Pair, does not fill a cell directly; it removes candidates. That is exactly what moves you forward in medium puzzles once the singles are used up. Watch for boxes where a candidate appears only two or three times and sits on one line.
If two cells in the same row, column or box hold exactly the same two candidates, they form a Naked Pair. The two numbers must go into those two cells, in whichever order. Everywhere else in the unit you can therefore remove them. The same principle works with three cells and three numbers as a Naked Triple, where not every cell needs to contain all three candidates. Clean notes are a prerequisite here; without them the pairs are easy to miss.
The Hidden Pair is the counterpart of the Naked Pair. Two numbers appear as candidates in only the same two cells of a unit, but those cells hold additional candidates. Since the two numbers have no other place to go, those two cells belong to them, and you can delete every other candidate in them. Hidden Pairs are harder to spot than Naked Pairs because they hide behind the surplus candidates. Scan the unit number by number rather than cell by cell.
For an X-Wing you look for two rows in which a candidate is possible in only two positions, and those positions share the same two columns. The four cells form a rectangle. Because the number must be placed in both rows, only two layouts exist: top left with bottom right, or top right with bottom left. The imagined diagonals draw the X of the name. Either way, the number is used up in both columns, so every other candidate for it in those two columns can be removed. The pattern works just as well with rows and columns swapped.
The Swordfish extends the X-Wing from two lines to three. You need three rows in which a candidate appears in no more than the same three columns overall. The number is then forced into those three columns, and you can remove it from all other rows in them. In practice the Swordfish is rare, but when an expert puzzle is completely stuck the search pays off: mark every remaining candidate of a single number across the grid, and the pattern becomes visible.
The XY-Wing works with three cells that hold exactly two candidates each. The pivot contains X and Y. It sees two wings, one with X and Z, one with Y and Z. Whichever number ends up in the pivot, one of the two wings is forced to take the Z. Any cell that sees both wings at once therefore cannot hold Z anymore. Seeing means sharing a row, column or box. The XY-Wing is among the strongest patterns that can still be found reliably by hand.
Reading alone does not make a solver. Pick one technique and hunt for its pattern deliberately, ideally at the level it was made for: singles in easy puzzles, Locked Candidates and pairs at medium, X-Wing and XY-Wing at hard or expert. The note mode in the game handles the candidate bookkeeping for you.
Always from simple to complex. Work through all Naked and Hidden Singles first, then check Locked Candidates and pairs. Only when nothing moves anymore is it worth searching for X-Wing, Swordfish or XY-Wing.
From the hard level onwards, practically yes. Techniques like Naked Pair or X-Wing assume you know the possible candidates per cell. Without notes these patterns are almost impossible to spot reliably.
For every puzzle on SudokuWelt.ch, yes. More exotic patterns such as Jellyfish or chained strategies exist, but fairly constructed puzzles up to expert level can be solved completely with these eight techniques.