Naked and Hidden Singles, Pairs & Triples Explained

If you learn just one family of Sudoku techniques, make it this one. Naked and hidden singles, pairs, and triples are the workhorses. Together they solve nearly every puzzle short of the expert tier. The names sound intimidating, but the ideas are simple once you see them, and the whole trick is understanding the difference between "naked" and "hidden."

So let's nail that first. Naked means a cell's candidates are exposed: you look at the cell, and the answer (or a useful group) is sitting right there in its own candidate list. Hidden means the answer is buried among other candidates, and you find it by looking at the whole row, column, or box instead of the single cell. Naked, look at the cell. Hidden, look at the unit. Keep that distinction and the rest follows.

Naked single

The simplest find in Sudoku. A naked single is an empty cell with only one candidate left. Its row, column, and box have eliminated every other digit, so one number is all that fits. Write it in.

You'll create naked singles constantly as you solve. Every digit you place removes candidates elsewhere, and sooner or later a cell drops to one option. After any cluster of placements, sweep for them first. They're free.

Hidden single

This is the technique that turns a beginner into a real solver. A hidden single is a digit that can go in only one cell within a row, column, or box, even though that cell still has other candidates listed.

Picture a row where the digit 4 appears in the candidate lists of just one cell. That cell might also show {2, 4, 7}, so it doesn't look solved. But 4 has nowhere else to go in the row, so the cell must be 4. Done.

Scanning often walks right past hidden singles, which is why medium puzzles feel harder than easy ones. They're built around exactly this move. To find them, pick a digit and a unit, and ask: how many cells in this unit could hold this digit? If the answer is one, you've found a hidden single.

Naked pair

Now we move to groups. A naked pair is two cells in the same unit (row, column, or box) that share the exact same two candidates, and only those two. For example, two cells both showing {3, 8}.

You don't know which cell is the 3 and which is the 8. But between them, they've claimed both digits for good. That means 3 and 8 can be erased from every other cell in that unit. Those erasures are where the magic happens: clearing candidates often exposes a naked single or a hidden single somewhere nearby, and the grid starts unraveling.

This is the bread and butter of hard Sudoku. Most hard puzzles come down to spotting one or two naked pairs at the right moment.

Hidden pair

The mirror image of a naked pair. Here, two digits appear in only two cells of a unit, but those cells are cluttered with other candidates too.

Say in one box, the digits 5 and 9 each appear in the candidate lists of only two cells, and they're the same two cells. Those two cells must hold the 5 and the 9 between them. So you can strip every other candidate out of those two cells, leaving just {5, 9} in each. Now you've effectively created a naked pair, and the eliminations continue from there.

Hidden pairs are harder to spot because nothing about the cells looks special at first. You find them by counting where each digit can live, not by staring at individual cells.

Naked and hidden triples

Triples are the same ideas stretched to three.

A naked triple is three cells in a unit whose candidates, combined, use only three digits. They don't each need all three. {2, 5}, {5, 7}, and {2, 7} is a valid naked triple, because between them they only involve 2, 5, and 7. Those three digits get erased from the rest of the unit.

A hidden triple is three digits that appear only within the same three cells of a unit, which lets you clear the other candidates out of those cells.

Triples are rarer and take more practice to see. Don't worry if they don't jump out yet. Most puzzles never require them, and when they do, the candidate grid usually nudges you toward them.

How to spot them faster

A few habits that help:

• Write clean, complete pencil marks. None of these techniques work without accurate candidates. See the pencil marks guide.
• Singles before pairs, pairs before triples. Always take the cheapest move available before hunting for a bigger pattern.
• Re-check the unit after every elimination. One naked pair can trigger a chain of singles, so don't move on too quickly.

Master this family and you've got the toolkit for the vast majority of grids. When even triples aren't enough, the next step up is X-Wing and the advanced techniques. For the full picture of how everything fits together, the strategy guide puts these moves in solving order.

Try it live: open a hard puzzle, fill in your candidates, and go hunting for that first naked pair.