Hidden Pairs and Triples in Sudoku: What to Do When the Basics Stop Working
Sudoku a Day Blog ·
You have filled in the obvious singles. Your pencil marks are neat. You have scanned every row, column, and box, and nothing new jumps out. Sound familiar?
This is the plateau most intermediate players hit. The basic techniques that carried you through easy and medium puzzles simply run out of steam on harder grids. The good news: you are probably one technique away from breaking through. Hidden pairs and hidden triples are the next tools you need, and once you see them, you will wonder how you missed them before.
What Is a Hidden Pair?
A hidden pair occurs when two candidates appear in exactly two cells within a single unit (a row, column, or box), and those two candidates are not found anywhere else in that unit.
The word "hidden" is key. Unlike a naked pair, where two cells contain only the same two candidates and nothing else, a hidden pair is buried among other candidates in those cells. The extra pencil marks act as camouflage, making the pair easy to overlook.
Worked example: Imagine a 3×3 box where five cells still have candidates. You notice that digits 3 and 7 only appear in two of those cells. Cell A has candidates {1, 3, 5, 7} and Cell B has candidates {2, 3, 7, 9}. Because 3 and 7 cannot go anywhere else in this box, they must occupy Cells A and B. Remove all other candidates from those two cells — Cell A becomes {3, 7}, Cell B becomes {3, 7}. That single elimination can unlock a chain of new singles across the grid.
Spotting Hidden Pairs Step by Step
- Pick a unit. Start with a row, column, or box.
- Count candidate appearances. For each missing digit in that unit, note which cells contain it as a candidate.
- Look for digits that appear in exactly two cells. If two different digits share the same two cells, and only those two cells, you have a hidden pair.
- Eliminate the extras. Remove every other candidate from those two cells. The pair is locked in.
Practical tip: focus on the digits, not the cells. Ask "Where can 4 go in this row?" instead of "What can go in this cell?" That shift makes hidden pairs far easier to spot.
Hidden Triples: The Same Logic, One More Cell
A hidden triple works just like a hidden pair, but with three candidates spread across exactly three cells in a unit. The tricky part: not every candidate needs to appear in all three cells.
Example — digits 2, 5, and 8 distributed in a column:
- Cell X: {2, 5, 6, 9} → becomes {2, 5}
- Cell Y: {1, 2, 8} → becomes {2, 8}
- Cell Z: {4, 5, 8} → becomes {5, 8}
If 2, 5, and 8 appear only in these three cells within that column, remove all other candidates from them. The rule only requires that the three candidates collectively occupy exactly three cells.
When to Look for Hidden Pairs and Triples
Use this solving order:
- Naked and hidden singles first — always exhaust these before anything else.
- Locked candidates — check for pointing pairs and box/line reduction.
- Hidden pairs and triples — when the grid feels stuck after the steps above.
On expert puzzles, expect to use hidden pairs at least once. On easier difficulties, you may never need them.
Common Mistakes
- Confusing hidden pairs with naked pairs. With naked pairs you eliminate from surrounding cells; with hidden pairs you eliminate from the pair cells themselves.
- Eliminating too broadly. Only remove extra candidates from the pair/triple cells — not from other cells in the unit.
- Forgetting overlapping units. After a hidden pair elimination, check whether new singles appear in the overlapping row/column/box.
Practice
The best way to internalize hidden pairs and triples is repetition. Try an expert sudoku puzzle on Sudoku a Day. For an even bigger challenge, explore master difficulty puzzles, where hidden triples appear regularly. Want a broader overview? Check our sudoku strategies guide for a complete progression from beginner to advanced.
Frequently Asked Questions
What is a hidden pair in sudoku?
A hidden pair is two candidates that appear in exactly two cells within a row, column, or box, and nowhere else in that unit. Other candidates may also be present in those two cells. Once identified, you can remove all other candidates from those two cells.
How do hidden pairs differ from naked pairs?
In a naked pair, two cells contain only the same two candidates. In a hidden pair, those two cells also contain other candidates. With naked pairs you eliminate from surrounding cells; with hidden pairs you eliminate the extra digits from the pair cells themselves.
How do I spot a hidden triple?
Look for three candidates that collectively appear in only three cells within a unit. Not all three candidates need to appear in every cell. If those three digits cannot be found anywhere else in the unit, you have a hidden triple.
When should I use hidden pairs vs other advanced techniques?
Use hidden pairs after you have exhausted singles and locked candidates. They are generally easier to spot than X-Wings or Swordfish, and they solve a large share of "stuck" moments on expert and master puzzles.