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Sudoku technique

Hidden pairs

Two digits with only two homes between them in a unit. The cells they live in are decided even though neither cell is solved — and everything else in those cells can go.

What a hidden pair is

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 therefore hold those two digits, in some order — which means every other candidate sitting in them is dead.

The cells might have looked wide open. A cell showing 2,4,6,7,9 can be half of a hidden pair on 4 and 9, and once you have spotted it, that cell drops to 4,9 in one move.

The mirror of a naked pair

A naked pair is two cells holding the same two candidates, and it eliminates outward — those digits leave the rest of the unit. A hidden pair is two digits holding the same two cells, and it eliminates inward — the other digits leave those two cells.

The two are the same fact viewed from opposite ends, and one usually creates the other. Once a hidden pair has stripped two cells down to two candidates, those cells are a naked pair, and the eliminations start flowing outward as well.

Why they are missed

Because nothing on the board looks unusual. A naked pair is visually obvious — two cells with two marks each, sitting in the same unit. A hidden pair is invisible until you stop reading cells and start tracking a digit across a unit, which is a different and less natural motion.

6
3
2
4
9
1
8
1
7
5
3
8
2
9
8
9
4
6
1
3
6
8
5
9
2
4
8
9
3
1
9
3
8
7
8
9
2
5
9
7
8
1
9
8
2
3

Step 1 of 4

A real position

Part way through a grid, with candidates marked. Nothing here is a single, and the obvious pairs have already been played.

A real position from a generated puzzle. Every elimination shown here was checked against that puzzle's actual solution.

How to find them

Work one unit at a time and count homes rather than candidates. For each digit still missing from the unit, note how many empty cells could take it. Ignore anything with three or more. Then look at the digits with exactly two homes and check whether any two of them share the same pair of cells.

Written down it is a short list — usually three or four digits per unit — and comparing them takes seconds. Trying to see it by staring at the grid does not work, which is why hidden pairs have a reputation for being hard.

Triples exist too

Three digits confined to the same three cells is a hidden triple, and it works identically: those three cells lose every other candidate. They are rare and genuinely difficult to spot, and by the time a board needs one there is usually an X-Wing available that is easier to see.

The practical advice is to look for hidden pairs deliberately and hidden triples only when a grid has stalled with nothing else on offer.

Other techniques

Try it on a real board

The free board on the home page has a notes mode, which is what every technique past hidden singles needs. Then take the same eye into a live match.