You know naked pairs, you scan the grid properly… and yet you get stuck on level 4 or 5 puzzles. The hidden pair is very likely the technique you are missing, and it is by far the most neglected of the basic techniques.
Its peculiarity: unlike the naked pair, which jumps out at you, the hidden pair is concealed among other candidates. You have to look for it actively to see it.
The exact difference between hidden and naked pairs (the number one source of confusion), how to apply it in a row, a column and a box, and the Domino33 method to spot it without spending ten minutes on it.
🎬 The Domino33 video on hidden pairs
Here is the full video, covering the technique in all three units: row, column and box.
▶ English audio track and English subtitles: pick either from the ⚙️ icon.
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Hidden pair or naked pair?
This is the most widespread confusion, and clearing it up changes everything.
- Naked pair: a cell is left with only 2 candidates. You then eliminate those 2 digits from the other cells of the unit.
- Hidden pair: 2 digits appear in only 2 cells of the unit, but those cells also contain other candidates. You then eliminate all the other candidates from those 2 cells.
The naked pair cleans the outside (the other cells). The hidden pair cleans the inside (the two cells themselves). Remember that sentence and you will never mix them up again.
Why “hidden”?
Because the pair is buried among other candidates. In a cell containing {1,4,7,9}, the pair {4,7} is far from obvious. It only reveals itself when you count where each digit can go across the whole unit.
A concrete example
Here is a row from a grid. Look at where the 4 and the 7 can go:
The 4 and the 7 appear only in C2 and C5. Yet both digits must be placed somewhere in the row: they will therefore necessarily occupy those two cells, in one order or the other.
Consequence: every other candidate in C2 and C5 is impossible and can be eliminated.
C2 goes from {1,4,7,9} to {4,7} · C5 goes from {4,6,7} to {4,7}
You have just created a naked pair where nothing was visible, and the 1, the 9 and the 6 are now freed up for the rest of the grid. That elimination is often what unlocks everything.
Part 2
In a row, a column and a box
The reasoning is strictly identical in all three units. Only where you count changes:
- In a row : the 9 cells of one horizontal line
- In a column : the 9 cells of one vertical line
- In a box : the 9 cells of one 3×3 square
Many solvers only look for hidden pairs in rows. They mechanically miss two thirds of them. Boxes are particularly productive, because candidates tend to be more concentrated there.
The video covers all three cases one after the other, with a dedicated example for each.
Part 3
The search method
Step 1, Choose a unit
A row, a column or a box. Work through it completely before moving to the next one: jumping between units is the best way to find nothing.
Step 2, Count the occurrences of each digit
For each digit still to be placed in that unit, count how many cells it is still a candidate in. Note, mentally or in the margin, those that appear in exactly 2 cells.
Step 3, Look for two digits sharing the same 2 cells
If two different digits appear only in the same two cells: you have a hidden pair. Eliminate all other candidates from those two cells.
Focus first on the rare digits of the unit, those with few placements left. Statistically they are the ones with only 2 possible cells, so they are the ones forming hidden pairs.
🎬 See the method in action
In the video, the method is walked through on real grids, in all three units. It is the fastest way to build the reflex.
Exercise
Your turn
Here is another grid row. It contains a hidden pair, somewhere other than in the example.
Count, for each digit, how many cells it can still go in.
Part 4
Application quiz
Four questions to check what you have learned. Good luck!
❓ Frequently asked questions
A naked pair is a cell left with only 2 candidates: you then eliminate those 2 digits from the other cells of the unit. A hidden pair is the opposite: 2 digits appear in only 2 cells of the unit, but those cells also contain other candidates. You then eliminate all the other candidates from those 2 cells. The naked pair cleans the outside, the hidden pair cleans the inside.
Because the pair is concealed among other candidates. In a cell containing {1,4,7,9}, the pair {4,7} is not visible at first glance: you have to count where each digit can go within the unit to uncover it.
In all three: a row, a column or a 3x3 box. The reasoning is identical in each case, only the unit examined changes. Many solvers only look in rows and therefore miss half of the hidden pairs.
It is a basic technique, useful from level 3 or 4 grids onwards and indispensable after that. It is one of the 6 fundamental techniques, alongside naked pairs, triples and Box Reduction. It often unlocks a grid where simple scanning no longer yields anything.
📋 Summary
Hidden pair essentials
- Setup: 2 digits appearing in only 2 cells of the same unit
- Action: eliminate all the other candidates from those 2 cells
- Do not confuse: the naked pair cleans the outside, the hidden pair the inside
- Starting point: count the occurrences of each digit in the unit
- Units: row, column and box, do not neglect the boxes
- Related techniques: hidden triples, Box Reduction, Pointing Pairs
The hidden pair takes a little more effort than the naked pair, which is exactly why it is still available when everything else is blocked. It is also the gateway to the advanced techniques, which all rest on the same candidate-counting work.
📘 Go further with the Domino33 books
Hidden pairs and all the other techniques on this site are covered step by step in the Domino33 memento, available in English.
