BrainPuzzles

Naked pair

Two cells in the same unit that can only be the same two digits. Between them they use both, which pushes those digits out of every other cell in that unit.

How to spot one

  1. Look for two cells in the same unit whose candidates are the same two digits.
  2. Those two digits have to go in those two cells, in one order or the other.
  3. So no other cell in that unit can be either of them. Cross both out everywhere else in the unit.

A real example

This grid is not a drawing. It came out of our generator, and the position below is one a solver actually reaches: every digit the reasoning uses is on the board, so you can check it yourself without taking anything on trust. The reasoning sits in row 1, shaded blue. The cells it looks at are green; the cells it changes are amber.

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Two cells in row 1 can only be 4 or 5, so between them they use both and no other cell in row 1 can be 4 or 5. So r1c1, r1c5, r1c6 lose those candidates.

The same move on a different grid

One example can be a fluke of the grid it sits in, so here is another, dug at hard from the seed second:naked-pair:100 with 28 starting digits. The technique fires in a different place, for a different digit, and the point is what it buys you afterwards.

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Two cells in row 2 can only be 2 or 9, so between them they use both and no other cell in row 2 can be 2 or 9. So r2c4 loses that candidate.

What the solver does next, from exactly that position:

  1. naked single — One cell in row 2 has a single candidate left, and it has to be 9. r2c3 takes 9, the only digit it had left.
  2. hidden single — In column 2, 9 has only one cell left it can go in. r8c2 takes 9, the only digit it had left.
  3. hidden single — In column 2, 5 has only one cell left it can go in. r4c2 takes 5, the only digit it had left.

That is the pay-off a naked pair is worth: not the one cell it names, but the run of cheap moves it unlocks behind it.

Where you meet it

Our grids are graded by the hardest technique they force, so a naked pair is what makes a hard grid what it is. Needs a pair or a locked digit. When you ask for a hint on one of them, the first thing the game says is the name of the technique and which row, column or box to use it in, and that step costs nothing — you still get to find the cell yourself.

The other techniques

Ready to use it? Play hard sudoku, take on the daily grid, or start from how to play.