Once you've mastered scanning and naked singles, Easy and Medium puzzles start to feel routine. But Hard and Expert sudoku require a different toolkit. This guide covers every major advanced technique, in order from most to least commonly used, so you can work through them systematically.
Before you start: Advanced techniques require pencil marks. If you aren't already marking candidates in empty cells, start now. Every technique below depends on being able to see which numbers are possible in each cell.
A hidden single is a cell where only one candidate appears in that position across its row, column, or box — even if the cell has other pencil marks.
How to find them: For each number, scan each row, column, and box. If a number appears as a candidate in only one cell within that unit, it goes there — regardless of what other numbers are also marked in that cell.
Why it's called "hidden": The decisive candidate is hidden among others. In a naked single, there's only one number possible. In a hidden single, the number is the only one that can go anywhere in its unit — but the cell itself may show 2–4 candidates.
Hidden singles alone will often break through a stuck Medium puzzle. Always check for them before moving to more complex techniques.
A naked pair is two cells in the same row, column, or box that both contain exactly the same two candidates — and nothing else.
What you can do: Those two numbers must go in those two cells. You don't know which way round, but you know neither number can go anywhere else in that unit. Remove both candidates from all other cells in the row, column, or box that contains the pair.
Example: Cells A and B in the same row both show only {3,7}. Every other cell in that row that contains a 3 or 7 can have those marks removed.
Naked pairs are the most commonly needed Hard technique. After placing hidden singles, always look for pairs before anything else.
A hidden pair is two numbers that appear as candidates in exactly two cells within a unit — and those two cells both contain those numbers, along with other candidates.
What you can do: Because those two numbers can only go in those two cells, all other candidates in those two cells can be removed. This turns the hidden pair into a naked pair, which you can then use to eliminate candidates elsewhere.
Hidden pairs are trickier to spot than naked pairs because the key numbers are mixed in with other candidates. Scan each unit for numbers that appear as candidates in only two cells.
Like naked pairs but with three cells and three numbers. Three cells in a unit that between them contain only three candidates (not all three need to appear in every cell — the union of their candidates equals exactly three numbers).
Example: Three cells show {1,2}, {2,3}, and {1,3}. Together they cover only 1, 2, and 3. These three numbers can be removed from all other cells in that unit.
Naked triples appear less often than pairs but are essential for harder puzzles.
When a candidate number appears in only one row or column within a 3×3 box, it must go in that row or column within the box. Therefore, you can eliminate that candidate from the rest of that row or column outside the box.
How to find them: Look at a 3×3 box. For each candidate, check whether all occurrences of that candidate within the box fall in a single row or a single column. If they do, eliminate that candidate from the rest of that row or column.
Pointing pairs are one of the most powerful Medium-to-Hard techniques because they create eliminations across a long row or column that you might not otherwise have connected.
The reverse of pointing pairs. When a candidate appears only within one box along a given row or column, you can eliminate that candidate from the rest of the box.
Example: Number 5 appears in a row only within the cells of one particular box. Since the 5 in that row must go somewhere in that box, you can remove 5 from all other cells in the box that aren't in that row.
X-wing is the gateway to expert-level sudoku. It involves four cells forming a rectangle across the grid.
The pattern: A candidate number appears in exactly two cells in Row A, and exactly two cells in Row B. If those pairs of cells are in the same two columns, you have an X-wing.
Why it works: The number must go in one of the two cells in Row A, and one of the two cells in Row B. Either way, both columns will contain the number. Therefore, you can eliminate that candidate from all other cells in those two columns.
Finding it: Look for a candidate that appears exactly twice in two different rows. Check whether those two pairs share the same columns. If yes, eliminate from the columns.
X-wing also works with columns instead of rows — look for a candidate appearing exactly twice in two columns that share the same rows, then eliminate from those rows.
Swordfish is X-wing extended to three rows and three columns. A candidate appears in 2–3 cells in each of three rows, and all those cells fall within the same three columns.
What you can do: Eliminate that candidate from all other cells in those three columns.
Swordfish is rare but occasionally essential for cracking Expert puzzles that resist all other techniques. The logic is the same as X-wing — the candidate must account for all three columns across the three rows, so it cannot appear elsewhere in those columns.
Y-wing involves three cells with exactly two candidates each, arranged so that one "pivot" cell sees both "wing" cells. The two wing cells share one common candidate that can be eliminated from any cell that sees both wings.
The pattern: Pivot has candidates {A,B}. Wing 1 has {A,C}. Wing 2 has {B,C}. The pivot sees both wings. Any cell that sees both Wing 1 and Wing 2 cannot contain C.
Y-wing is one of the most elegant techniques in sudoku and frequently appears in Expert puzzles. Once you start seeing the pattern, it becomes almost satisfying to spot.
When you're stuck on a Hard or Expert puzzle, work through this checklist in order:
Most Hard puzzles are solved by step 5. Expert puzzles often require X-wing or Y-wing. If you've gone through all eight steps and are still stuck, go back to step 1 — placing a number often unlocks new eliminations you couldn't see before.
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