Once you've mastered scanning, crosshatching, and lone singles, you'll find that harder puzzles come to a standstill. The basic techniques don't reveal any new numbers, and you're staring at a grid full of candidates. This is where advanced strategies come in — they don't place numbers directly, but they eliminate candidates, which eventually leads to a placement.
Every technique in this article is based on pure logic. There is no guessing — only deduction.
Prerequisites: Candidate Notation
All advanced techniques require you to first populate every empty cell with its candidate list — the set of numbers that could legally go there given the current state of the grid. In Sudoku Dark, tap the pencil icon to enter note mode. The app will track your notes as you solve.
Once candidates are in place, patterns become visible that would otherwise be invisible.
1. Naked Pairs
IntermediateNaked Pairs
If exactly two cells in a row, column, or box each contain the same two candidates — and only those two candidates — then those two numbers must go in those two cells (in some order). Therefore, you can eliminate both candidates from every other cell in that row, column, or box.
Example: Suppose in a row, two cells both show candidates {3, 7} and no other cells contain only 3 and 7. You don't know which cell holds 3 and which holds 7, but you know for certain that no other cell in that row can contain 3 or 7. Remove them from all other candidates in the row.
Naked pairs are among the most common advanced eliminations. Once you start looking for them, you'll spot them frequently in medium-difficulty puzzles.
2. Hidden Pairs
IntermediateHidden Pairs
If two numbers appear as candidates in exactly two cells of a row, column, or box — even if those cells also have other candidates — then those two numbers must go in those two cells. You can eliminate all other candidates from those two cells.
Example: In a column, the numbers 4 and 9 both appear as candidates in exactly two cells. One of those cells might show {2, 4, 7, 9} and the other {1, 4, 9}. Because 4 and 9 can only go in these two cells, the pair is "hidden" among the other candidates. You can strip out 2, 7, and 1 from those cells, leaving {4, 9} in both — which is now a naked pair, fully solved.
3. Pointing Pairs (Locked Candidates)
IntermediatePointing Pairs / Locked Candidates
If all the candidates for a particular number within a 3×3 box happen to lie in the same row or column, then that number cannot appear anywhere else in that row or column outside the box.
Example: In the top-centre box, the only cells that can hold the number 5 are in row 2. Therefore, the number 5 cannot appear in row 2 in any other box. Remove 5 from all other cells in row 2 outside this box.
The reverse also applies: if all candidates for a digit in a row are confined to a single box, you can eliminate that digit from the rest of the box.
4. Naked Triples
AdvancedThe naked pair logic extends to three cells. A naked triple occurs when three cells in a row, column, or box collectively contain only three candidates (distributed across the cells in any combination). For example, cells with {1,2}, {2,3}, and {1,3} form a naked triple — together they hold candidates 1, 2, and 3, and none of these can appear in any other cell in that group.
Key Insight
Each cell in the triple doesn't need all three candidates — just the union of candidates across the three cells must equal exactly three numbers.
5. X-Wing
AdvancedX-Wing
If a candidate digit appears in exactly two cells in each of two different rows, and those cells share the same two columns, then that digit must go in one of the two "diagonal" configurations. As a result, you can eliminate that candidate from all other cells in those two columns.
Example: Suppose the digit 6 can only appear in columns 2 and 7 within both row 1 and row 5. The four cells form a rectangle. No matter which diagonal holds the 6s, column 2 and column 7 already account for their 6s from these rows — so eliminate 6 from all other cells in columns 2 and 7.
X-Wings are a breakthrough moment for most solvers. They work because the four corner cells form a closed system: two rows and two columns each needing exactly one of the digit, and the four cells are the only possibilities across both rows.
6. Swordfish
ExpertSwordfish is X-Wing scaled up to three rows and three columns. If a candidate digit appears in at most two or three cells in each of three rows, and those cells are all confined to the same three columns, the digit's placements in those three columns are locked. Eliminate the digit from all other cells in those three columns.
Swordfish is rare and difficult to spot, but it's satisfying to apply. Most expert-level puzzles that appear unsolvable without guessing can be broken open with a Swordfish — if you're patient enough to find it.
7. Y-Wing (XY-Wing)
ExpertY-Wing
Pick a pivot cell with exactly two candidates, say {A, B}. Find two other cells (the wings) that each share a unit (row, column, or box) with the pivot and contain {A, C} and {B, C} respectively. Regardless of which value the pivot takes, C must appear in one of the two wing cells. Any cell that sees both wing cells can have C eliminated.
Y-Wing is the first technique that works across multiple units simultaneously, which is why it feels more "creative" than the pattern-based techniques above. Learning it is a major milestone.
When to Use Each Technique
In practice, you should work through techniques in order of difficulty — don't jump to Swordfish when naked pairs might still apply. A good solving order is:
- Full candidate notation
- Naked singles → Hidden singles
- Naked pairs → Hidden pairs
- Pointing pairs / locked candidates
- Naked triples → Hidden triples
- X-Wing
- Swordfish / Y-Wing
If you reach step 4 and stop making progress, it's time to look harder at the same level, not to skip ahead. Often a pair or triple is hiding in plain sight.
Apply These Techniques Right Now
Sudoku Dark's built-in note mode gives you full candidate tracking. Try Expert mode — it's designed to require the techniques in this article.
Play Expert Mode — Free