Pointing pairs and triples: when a box points along a line

What is a pointing pair?

Take one box and one digit that is still missing from it. Look at the empty cells in the box where that digit is a candidate. If those cells all sit in the same row, or all in the same column, they form a pointing pair (two cells) or a pointing triple (three cells).

The box “points” along that line: the digit is locked into the part of the line that passes through the box. Every other cell of that row or column, outside the box, can lose the digit as a candidate.

Why the elimination is safe

The box must contain the digit exactly once, and every possible place for it lies on one line. So whichever cell ends up holding it, the digit will be on that line inside the box. Since the line can hold the digit only once, no cell of the line outside the box can have it. You do not need to know which of the two or three cells is correct; the elimination holds either way.

How to find pointing pairs

This technique needs pencil marks, because it works on candidates. Once your candidates are complete and up to date, go box by box and digit by digit, and ask: do all the candidates for this digit in this box share a row or a column?

You can also spot many pointing pairs without full pencil marks. Use the same cross-hatching you use for hidden singles: when a digit is blocked in a box everywhere except two or three cells on one line, that is a pointing pair even though it did not give you a single.

After you find one, check the rest of the line for that digit. If none of those cells had it as a candidate, the pattern is true but useless, so move on. When it does remove a candidate, look at the affected cells right away, because an elimination often creates a new naked or hidden single.

Worked example

In the example board, look at the bottom-right box, box 9. Its empty cells and candidates are R7C9 (row 7, column 9) with 1 and 7, R8C9 with 1, 7 and 8, and R9C7 and R9C8, both with 8 and 9. The 1 in R9C6 blocks row 9, so digit 1 can only go in the two highlighted cells, R7C9 and R8C9.

Both cells are in column 9. That means the 1 of box 9 will be in column 9, so no other cell of column 9 can be 1. The only other empty cell in column 9 is R6C9, which had candidates 1 and 8. Removing 1 leaves only 8.

R6C9 is now a naked single and must be 8, shown in gold. Before the pointing pair, 8 could also go in R6C3 or R6C8 in its row, so no single was available anywhere on the board. One elimination was enough to restart the solve.

Common mistakes

Missing a candidate in the box. If a third cell in the box can also hold the digit but is off the line, there is no pointing pair. Check every empty cell of the box, not just the two you noticed first.

Eliminating inside the box. The digit is removed only from the line outside the box. The cells of the pair keep the candidate, and other cells of the box were already free of it.

Mixing it up with box-line reduction. In a pointing pair the box restricts the line. In box-line reduction it is the other way round: a row or column confines the digit to one box, and you eliminate inside that box. Both are locked candidates, but the direction matters.

When to use it and what comes next

Reach for pointing pairs when singles run out. Quietdoku’s Medium puzzles are built around exactly this moment: they need pencil marks and locked candidates, but nothing harder. A Quietdoku hint will name locked candidates when that is the next step.

Learn box-line reduction next, since it is the mirror image of this technique. After that come naked pairs and hidden pairs, which you will meet in Hard puzzles.