Subsets & Locked Candidates
Hidden Pair
A Hidden Pair is two digits that, within one row, column or box, can only go in the same two cells. Those two cells must take the two digits, so every other candidate in them is removed, while the rest of the unit is left as it is. You find it by reading the unit digit by digit rather than cell by cell, and once the extras are gone the two cells form a Naked Pair.
What you need to see on the grid
Look for a Hidden Pair once singles and locked candidates have stopped producing moves and no Naked Pair shows up, in a unit whose cells are crowded with pencil marks. It is worth the count mainly in units with six or more empty cells — with fewer, the cells outside the pair form a naked pair or triple that you will usually see first. Four terms carry the method:
- Places of a digit
- For a digit still missing from the unit, the cells where it is still a candidate. A digit of a Hidden Pair has exactly two: one place is a Hidden Single, and three can never fit into two cells.
- The same two cells
- Both digits must point to the identical pair of cells. Two digits with two places each that share only one cell are not a pair — each can still take its other cell.
- The extra candidates
- The other digits pencilled into the two cells. They are what hides the pair — the cells look like any other busy cell — and they are exactly what the technique erases.
- The Naked Pair it leaves
- Once the extras are gone, the two cells hold only the two digits: a Naked Pair. It can clear those digits from any unit the two cells share, but in the pair's own unit they had no other places anyway, and a shared box or line has normally been cleared already by Locked Candidates.
How to apply it, step by step
One example runs through all five steps: row 2, part-way through a puzzle, with seven of its cells still empty. Every diagram shows the whole grid. The cells a step needs are filled in; the others are left blank and hatched, so you know you can ignore them. A digit missing from a drawn cell is one that its row, column or box already holds, even where that column or box is not drawn, or one that Locked Candidates has already removed.
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Step 1Scan one unit digit by digit and count each digit's places
Choose a row, column or box and go through the digits it is still missing, one at a time, noting the cells where each one is still a candidate. Row 2 here is missing 1, 2, 3, 4, 5, 8 and 9: 1 can go in C4, C6, C7 and C8; 2 in C4, C5, C6, C7 and C8; 3 in C2 and C7; 4 in C5 and C6; 5 in C2, C4, C5, C8 and C9; 8 in C5 and C6; 9 in C7 and C9.
Keep only the digits with exactly two places: 3, 4, 8 and 9. A digit with one place would be a Hidden Single, to be placed at once; a digit with three or more places cannot belong to a pair. This count is the whole trick — read cell by cell, R2C5 and R2C6 are just two cells with four candidates each.
Only row 2 matters here. 3, 4, 8 and 9 each have exactly two places and are highlighted; 1, 2 and 5 have four or five. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 7 6 R3 R4 R5 R6 R7 R8 R9 - Digit already on the grid
- Row being read
- A place for a digit with two places
- Candidates 3, 4, 8 and 9, the digits studied
- Not needed for this step
Filled in: row 2. The other 72 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.
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Step 2Find two of them that share the same two cells
Compare the places of the digits you kept. 4 sits in R2C5 and R2C6, and so does 8: the same two cells. Row 2 must contain both 4 and 8, and neither has anywhere else to go, so R2C5 and R2C6 are the cells that will hold them — one each, even though we do not know yet which goes where. That is a Hidden Pair.
3 and 9 also have two places each, but not the same two: 3 is in C2 and C7, 9 in C7 and C9. They share only R2C7, which proves nothing — 3 can still end up in C2 and 9 in C9. The real pair is hidden because R2C5 also lists 2 and 5, and R2C6 lists 1 and 2.
Technique: Hidden Pair
Row 2 in full. 4 and 8 appear only in R2C5 and R2C6; no other cell of the row lists either of them. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 7 6 R3 R4 R5 R6 R7 R8 R9 - Digit already on the grid
- Highlighted unit
- A cell of the pair
- Candidates 4 and 8, the digits studied
- Not needed for this step
Filled in: row 2. The other 72 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.
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Step 3Clear every other candidate from the two cells
R2C5 and R2C6 are taken by 4 and 8, so no other digit can go in either of them. Erase the extras: 2 and 5 from R2C5, 1 and 2 from R2C6. Keep 4 and 8 in both cells — the pair says which two digits the cells hold, not which cell takes which.
Leave the rest of the row alone. 4 and 8 never had a candidate in the other five empty cells — that is what made the pair — so there is nothing to remove there. The whole move happens inside the two cells.
Technique: Hidden Pair
Row 2 in full. The four extra candidates leave R2C5 and R2C6; the rest of the row is untouched. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 7 6 R3 R4 R5 R6 R7 R8 R9 - Digit already on the grid
- Highlighted unit
- A cell of the pair
- Candidates 4 and 8, the digits studied
- Candidate removed
- Not needed for this step
Filled in: row 2. The other 72 cells are left blank: they are not needed for this step. Removed: 1 from R2C6; 2 from R2C5 and R2C6; 5 from R2C5.
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Step 4Read the result: the two cells are now a Naked Pair
After the clean-up R2C5 and R2C6 both read {4,8} and nothing else: the Hidden Pair has become a Naked Pair, two cells with the same two candidates. It is the same fact seen from the other side — before, the two digits had two places each; now the two cells have two candidates each.
A Naked Pair removes its two digits from every other cell of any unit both cells share, here row 2 and box 2. Do not expect a second wave from it, though. In row 2, 4 and 8 had no other places anyway: that is how the pair was found. In box 2 the open cells outside row 2, R1C4, R1C6 and R3C4, list no 4 or 8 either, and on a grid where Locked Candidates has been played that is always so: once 4 and 8 are confined to the part of row 2 inside box 2, claiming has already removed them from the rest of the box. The payoff of this move is the four candidates you just erased.
Row 2 after the clean-up, with box 2. R2C5 and R2C6 read {4,8}; no other cell of row 2 or box 2 lists 4 or 8. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 9 R2 7 6 R3 6 3 R4 R5 R6 R7 R8 R9 - Digit already on the grid
- Row 2 and box 2, the units both cells share
- The Naked Pair {4,8}
- Candidates 4 and 8, the digits studied
- Not needed for this step
Filled in: row 2; box 2. The other 66 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.
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Step 5Collect what the erased candidates unlock
A Hidden Pair never places a digit by itself, so check each candidate it removed in the other units of its cell. R2C5 lost its 5. In column 5, 5 had only two places, R2C5 and R4C5; now R4C5 is the only one left, so R4C5 is 5: a Hidden Single.
The other removals — 2 from R2C5, 1 and 2 from R2C6 — still leave each of those digits two or more places in every row, column and box of those cells, so they create no other single. That is the usual pattern: you erase a handful of candidates, and one of them leaves a row, column or box with a single place for its digit.
Technique: Hidden Single
Column 5 after the Hidden Pair. With 5 gone from R2C5, it fits only R4C5. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 9 R2 R3 6 R4 5 R5 R6 R7 R8 R9 - Digit already on the grid
- Column 5: one place left for 5
- The cell that must be 5
- Candidate 5, the digit studied
- Digit placed
- Not needed for this step
Filled in: column 5. The other 72 cells are left blank: they are not needed for this step. Placed: R4C5 = 5.
Common mistakes
Pairing digits that also live elsewhere
Two digits showing up together in two cells is not enough: neither may appear anywhere else in the unit. In the example, R2C5 and R2C6 both list 2 as well, yet 2 is no partner for 4 or 8 — it also fits C4, C7 and C8. Check all nine cells of the unit for both digits before you erase anything.
Two places each, but not the same two
In row 2, 3 sits in C2 and C7 and 9 in C7 and C9. Both have two places and they overlap in R2C7, which makes them look like a pair. They are not: three cells are involved, and nothing stops 3 from taking C2 and 9 from taking C9. Both digits must name the very same two cells.
Clearing the rest of the unit instead
That is the Naked Pair move, read the wrong way round. The two digits of a hidden pair already have no candidates outside its two cells, so there is nothing to erase there; the move is to delete the other digits inside the two cells.
Learn the move, not just the digit
In a real game, the hint in the app shows the next cell you can fill and explains why that digit must go there. When a Hidden Pair made it possible, the explanation names the Hidden Pair, or another pattern that removes the same candidate, such as the naked set on the other side of the unit.