Pointing pairs

A pointing pair happens when, inside one box, a digit can only go in cells that all lie in the same row (or the same column). The digit must be in that box somewhere, so it must be in that row within the box, and the rest of the row outside the box cannot hold it. The pair “points” along the row and clears the digit from it. With three cells in a line it is called a pointing triple; the logic is identical.

Pointing pairs are by far the most common medium technique: in our medium bank, most puzzles use at least one. Together with box/line reduction, they are often called “locked candidates”.

Why it works

Say box 1 still needs a 6, and the only empty cells in box 1 where a 6 could go are in row 2. Whatever happens, the box's 6 will be in row 2. Row 2 can only have one 6, so no cell of row 2 outside box 1 can be 6. Those candidates can be removed, even though you still do not know exactly where in box 1 the 6 goes.

The reverse situation is called box/line reduction (or claiming): if a row's only possible cells for a digit all fall inside one box, the digit can be removed from the rest of that box. Our solver treats the two as separate techniques, both at the medium level.

How to spot it

• Look at one box and one digit at a time. Where can the digit go in this box? If all the spots are in a single row or column, you have a pointing pair or triple.
• Pencil marks make this fast: look for a box where a digit’s notes sit in a straight line.
• Then follow the line out of the box. Any note for that digit in the same row or column, outside the box, can be crossed out.
• Repeat after each elimination: clearing a digit from a row often creates a hidden single for it in another box.

Common mistakes

• Eliminating inside the box. The pointing cells say nothing about other cells in the same box; only cells outside the box, on the same line, lose the candidate.
• Using a box where the digit already has a cell outside the line. All of the box’s possible cells for that digit must be on the line.
• Confusing it with box/line reduction. Pointing starts from the box and clears the line; box/line reduction starts from the line and clears the box.

Related techniques

Pointing is the simplest example of a powerful idea: a digit “locked” into part of a unit can be removed from overlapping units. The naked pair and hidden pair lock digits into cells instead. The X-Wing, one of our hard techniques, locks a digit into two rows and clears it from two columns, which is the same reasoning on a bigger scale.

Stuck on a real puzzle? The sudoku solver names every technique it uses, step by step, and the hint button in the game teaches the same way.

How to practise

Play the three practice puzzles below in order. Each one reaches a point where pointing pairs are the only way forward with the medium-level toolbox, so if you get stuck, that is the moment to look for the pattern. Try first without help. If you still cannot see a move, press Hint once: the first level names the technique, the second shows where to look, and only the third makes the move for you. After you finish, play a few medium puzzles without hints to make the habit stick.