If you've mastered the basics — scanning for singles, filling obvious cells — but hard and expert puzzles still leave you stuck, you've hit the wall that every intermediate player reaches. The good news: a small set of named techniques will unlock almost any puzzle you'll ever encounter. Here's the complete guide to intermediate and advanced sudoku strategies.
Before you start: These techniques assume you're comfortable with candidate notation — penciling in every possible number for each empty cell. If you haven't used candidates before, start there. These patterns are invisible without them.
A naked pair occurs when exactly two cells in the same row, column, or box both contain only the same two candidates — and no others. When this happens, those two numbers must go in those two cells (you just don't know which order yet). Because they're "reserved" for those cells, you can safely eliminate those same numbers from every other cell in the shared unit.
Suppose in one row, two cells each show only {3, 7} as candidates. Every other cell in that row can have 3 and 7 removed from their candidate lists. This often triggers a cascade — removing candidates from one cell reveals singles in others.
Naked pairs are the most common advanced technique and should be the first thing you look for when singles dry up. Look row by row, then column by column, then box by box. A naked pair in a box that also shares a row or column with its partner can eliminate candidates in two directions simultaneously.
The flip side of naked pairs. A hidden pair exists when exactly two candidates appear in only two cells within a unit — even if those cells also have other candidates. Because those two numbers can only go in those two cells, all other candidates in those two cells can be eliminated, turning them into a naked pair.
Hidden pairs are harder to spot than naked pairs because they require you to look at where each number can go, rather than what numbers a cell contains. Scanning by candidate — "where can 5 go in this row?" — is the key habit.
The same logic extends to three cells. A naked triple means three cells in a unit collectively contain only three candidates, distributed among them in any combination. For example: {1,2}, {2,3}, {1,3} — three cells, three candidates, none repeated beyond the three cells. All three numbers can be eliminated from the rest of the unit.
Hidden triples follow the same pattern in reverse: three candidates each appear in only three cells within a unit. All other candidates in those three cells can be removed. Triples are rarer than pairs but appear consistently in hard puzzles.
When a candidate in a box is restricted to one row or one column within that box, that candidate can be eliminated from the rest of that row or column outside the box. The cells "point" in a direction, telling you where the number cannot go elsewhere.
If the number 4 can only go in two cells within a box, and both those cells are in the same row, then 4 must go in one of those two cells. That means 4 cannot appear anywhere else in that row outside the box. Remove it from all other row cells.
X-wing is the first of the "fish" techniques and one of the most satisfying to find. It applies when a single candidate appears in exactly two cells in each of two separate rows — and both rows share the same two columns for that candidate.
When this configuration exists, that candidate must appear in one of the two diagonal patterns: either the top-left and bottom-right cells, or the top-right and bottom-left cells. Either way, the number occupies one cell from each column. This means you can eliminate that candidate from every other cell in both columns.
X-wing rule of thumb: If you find a candidate that appears in exactly 2 cells in two different rows, check whether those 4 cells form a rectangle. If they do, you have an X-wing and can eliminate that candidate from the columns outside the rectangle.
X-wing also works in columns — the exact same pattern, rotated 90 degrees. If a candidate appears in exactly 2 cells in each of two columns, and those pairs share the same two rows, eliminate the candidate from all other cells in those rows.
Swordfish is X-wing extended to three rows (or columns). A swordfish exists when a candidate appears in exactly 2 or 3 cells in each of three separate rows, and those cells collectively occupy only three columns. The candidate must be placed in those three columns via those three rows — so it can be eliminated from all other cells in those three columns.
Swordfish is rare in easy and medium puzzles but appears regularly in expert-level grids. When you're stuck on expert and X-wing hasn't helped, systematically check for swordfish by listing which columns contain each candidate in every row.
Beyond swordfish sits jellyfish (4 rows, 4 columns). In practice, if a puzzle requires jellyfish, it's likely solvable earlier with another technique. Swordfish is the practical upper limit for most human solvers.
XY-wing involves three cells, each containing exactly two candidates. The pivot cell shares one candidate with each of the two wing cells, but the two wing cells share a different candidate with each other. If both wings can "see" a target cell (meaning they share a row, column, or box with it), the shared candidate between the wings can be eliminated from that target cell.
XY-wing is more complex to explain than to find with practice. Once you train your eye to look for cells with exactly two candidates, the pattern becomes recognisable.
Practice tip: When you find a technique that works, pause and understand why before moving on. The pattern recognition builds faster than rote memorisation.
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