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Pointing Pair

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Pointing Pair

All remaining places for a digit inside a box lie on one row or column, so the digit leaves the rest of that line.

The pattern

Look at one box and one digit that is still missing from it. If every cell that could hold that digit sits on the same row, then the digit is going somewhere on that row inside this box. It cannot also appear on that row in the two other boxes, so you can erase it there.

Two candidate cells make a pointing pair, three make a pointing triple. The logic is identical; only the count changes.

How to scan for it

This is a digit-first technique, not a cell-first one. Pick a digit, take each box where it is still missing, and mark the cells where it could go. If they all share a row or a column, you have an elimination — and the payoff lands outside the box, in the two boxes the line passes through.

Boxes that already have six or seven digits are the best hunting ground, because a missing digit rarely has more than two or three homes left in them.

Why it is valid

Every box must contain the digit. If all its possible positions in this box lie on one line, the box will place it on that line. A line holds each digit once, so the rest of the line — the part running through the other two boxes — is finished with that digit before you place anything.

The move that opens Hard puzzles

Together with box/line reduction, this is the elimination Hard puzzles on this site are built around: the solver needs one or two such steps and no advanced pattern. When a Hard grid stops producing singles, a pointing candidate is usually the reason it will start again.