Pointing Pairs and Box/Line Reduction

Also called "locked candidates", these two patterns are the first techniques that work with notes instead of placed numbers. They don't place a number directly; they remove candidates, which then reveals new singles.

Pointing pairs

Look inside one box at a single number's candidates. If all of them sit in the same row (or the same column), then that number must end up somewhere in that row inside this box. That means it cannot appear anywhere else in that row, outside the box.

Unit being checkedThe pair / patternCandidates removed

In the example, the top-left box still needs a 7. The 7 lower down in the first column rules out every cell in that column, and the four given numbers fill the rest of the box's bottom two rows. The only cells left for 7 are the two green ones, and both are in the top row.

Whichever of those two cells turns out to be the 7, the top row's 7 is inside this box. So any 7 candidate elsewhere in the top row can be crossed out, shown in red.

If three candidates line up instead of two, the logic is identical. That is called a pointing triple.

Box/line reduction (claiming)

Box/line reduction is the same idea in reverse. Start from a row or column instead of a box. If a number's candidates in that row all fall inside one box, then the box's copy of that number must be in that row. You can remove the number from the other cells of that box.

For example, suppose the only places for 4 in the fifth row are two cells in the middle box. The middle box's 4 must therefore be one of those two cells, so 4 can be removed from the other six cells of the middle box.

How to spot them

• Go box by box and number by number. You are looking for a number whose candidates form a short straight line.
• Pointing pairs are especially common right after you place a number that blocks one row or column of a box.
• After each elimination, look again for singles in the affected row or column. That is usually where the payoff is.

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