Lesson 4 of 8
Naked pair
A naked pair is two cells in the same unit holding the same two candidates, and nothing else. Between them they must use both digits, in one order or the other, so no other cell in that row, column or box can hold either of them.
- Level
- Intermediate
The pattern
Naked pair: what it does.
Two cells that read {4, 7} and {4, 7} are a pair. Whichever way round they end up, one of them is the 4 and the other is the 7, and the unit has spent both digits.
That makes the pair a small piece of certainty inside an uncertain unit, and everything it proves can be taken from the other seven cells.
Example
Naked pair: a worked example.
Look for matching two-mark cells
Scan a row, a column or a box for two cells carrying exactly the same two pencil marks. They don't need to be beside each other; they only need to share the unit.
Check neither cell can take more
The pair only holds if both cells stop at those two digits. A cell reading {4, 7, 9} that happens to contain the same two digits isn't part of the pair, and the eliminations below would be wrong.
Remove both digits from the unit
Delete the pair's two digits from every other cell of the row, the column or the box. You aren't placing the 4 or the 7 yet, only clearing the ground.
Follow what it uncovers
The removals often leave a single candidate behind, or expose a second pair in a unit that crosses the first. Place whatever has become certain before looking further.
Every empty cell with its candidates written in. Nothing is marked yet.On this board, the pattern sits in r3c2 and r9c2.It removes 4 from r1c2, r5c2, r6c2, and r7c2 and 9 from r1c2 and r7c2.
Video
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Spotting it
Naked pair: how to spot it.
- Cells with only two pencil marks are the raw material. Fill the grid with complete candidates and pairs announce themselves.
- Pairs turn up most often in boxes that are half filled, where two cells have been squeezed down to the same two digits.
- One pair frequently sits next to another: a naked pair in a box often clears the way for a single in the row that crosses it.
Where it stops working
The two cells have to share a unit and both have to carry exactly two candidates. Any extra candidate in either cell voids the pair, and an extra candidate elsewhere in the unit is exactly what the technique is designed to remove. If you can't see the same two digits in both cells, you're looking at something else.
Keep going
Related topics.
New to sudoku? The rules take two minutes to read, and the first-puzzle walkthrough covers the basics that come before any of these.
Practice it in Sudoku Mori.
Naked pair is lesson 4 in the game, with a worked example and three exercises, part of Sudoku Mori Full. Lesson puzzles are separate from your daily ones, and you can redo any lesson whenever you like.
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