Naked pairs and hidden pairs in sudoku
What a naked pair removes, what a hidden pair removes, why they are opposites, and the mistake that makes players think a hidden pair does nothing.
Naked pair and hidden pair are the two techniques where sudoku stops being about scanning and starts being about candidates. They are usually taught one after the other, which is why so many people can recite both definitions and still not know which one they are looking at.
The distinction is easier than the names suggest. A naked pair removes digits from other cells. A hidden pair removes other digits from these cells. That single sentence is the whole difference.
Naked pair
A unit is a row, a column or a box — nine cells that must contain the digits 1 to 9 exactly once each.
A naked pair is two cells inside one unit whose candidate lists are identical and consist of exactly two digits. Say two cells in a row can each only be 4 or 9, and nothing else.
You do not know which of the two cells holds the 4 and which holds the 9. You do not need to. Between them, those two cells will consume both digits: there are two cells, two digits, and neither digit can go anywhere else within the pair. So the 4 and the 9 are spoken for.
Therefore no other cell in that row can be a 4 or a 9. Cross both digits out of the other seven cells. That is the elimination, and it is why the pattern is called naked: the two digits are sitting there in plain sight in both cells.
The condition people get wrong
Both cells must have exactly two candidates. If one cell reads 4 or 9 and the other reads 4, 9 or 6, that is not a naked pair and the elimination is invalid — the second cell might genuinely be a 6, leaving the 4 and 9 needing a home elsewhere in the unit. This is the single most common way to wreck an otherwise sound grid, because the resulting contradiction usually surfaces twenty moves later, far from the cause.
Hidden pair
A hidden pair works from the other direction. Instead of looking at the cells, look at the digits.
Find two digits in a unit that between them can only go in the same two cells. Say in one box, 3 can only be placed in cells A and B, and 7 can also only be placed in cells A and B. The two cells may have plenty of other candidates written in — that is what makes the pair hidden.
The box needs a 3 and it needs a 7, and both only fit in A and B. So A and B are taken: one is the 3, the other is the 7. Every other candidate in A and B is therefore impossible, and you delete them all.
Notice what happened. A naked pair cleaned the rest of the unit. A hidden pair cleaned these two cells. The evidence is the same shape; the conclusion points the opposite way.
Why hidden pairs feel like they do nothing
A hidden pair never places a digit and never touches any cell except the two in the pair. If you are scanning for progress on the board, it looks like nothing happened. What it actually did was turn two crowded cells into a naked pair — because after the cleanup, A and B contain exactly 3 and 7 and nothing else.
That is the real payoff, and it is why solvers run hidden pair after naked pair rather than before: the hidden pair manufactures the naked pair, and the naked pair then cleans out the rest of the unit. One deduction, two stages.
Triples, and where this stops
Both patterns generalise. A naked triple is three cells in a unit whose candidates are drawn from the same three digits — each cell needs only two of the three, not all three, which is the part people miss. A hidden triple is three digits confined to the same three cells. The logic is identical: three cells, three digits, no room for anything else.
Beyond triples the returns fall off quickly, because a naked quad in a nine-cell unit implies a hidden pair among the remaining five cells, and that is usually easier to see. This is why most solvers, including the one in Sudoku - Calm Number Puzzle, stop at triples and move on to pattern techniques like X-Wing instead.
Where they sit in difficulty
These techniques are what separate a medium puzzle from a hard one. In this app the grade of a puzzle is the hardest technique the solver actually needed: naked pair, pointing and claiming land a puzzle in Medium, while hidden pair and naked triple push it to Hard. Nothing beyond triples is required until the Expert band.
Frequently asked questions
Can a naked pair and a hidden pair be the same two cells?
Yes, and that is exactly what happens after you apply a hidden pair. Once the extra candidates are stripped out, those two cells hold exactly two digits each, which is the definition of a naked pair. The two patterns are the same situation seen before and after cleanup.
Does a naked pair work across a row and a box at once?
If both cells share a row and also share a box, then both units qualify and you can eliminate in both. That is common and worth checking for — the box elimination is the one people forget.
Why do my pencil marks get worse after applying a pair?
They should get strictly smaller, never larger. If candidates appear that were not there before, either auto-fill recomputed the whole grid from a wrong digit you entered earlier, or the pair was not valid — usually a cell with three candidates treated as if it had two.
Do I need pencil marks to use these?
For naked pairs, not necessarily — with practice you can see a two-candidate cell without writing it down. For hidden pairs, effectively yes, because the whole pattern is about which cells a digit can still occupy, and that is not visible without the candidate grid in front of you.
Try it on a real puzzle
Sudoku - Calm Number Puzzle grades every puzzle by the hardest technique it actually needs, verifies a single solution before you ever see the grid, and its hints name the technique instead of just filling in a digit. Free, offline, no ads and no account.