Sudoku Clan › Sudoku techniques › Pointing pairs
Pointing pairs in Sudoku
- Intermediate
- Needed from Expert puzzles
- 2 points in Duel
Also called pointing triples or locked candidates type 1.
When all the places a digit can go inside a box lie on one row or column, the digit is locked to that line, and it can be removed from the rest of the line outside the box.
How it works
A box must contain each digit once. Suppose that inside one box the digit 5 can only go in two cells, and both are in the same row. You do not know which of the two will be the 5, but you know the 5 of that row will be inside this box. So no other cell of that row can be a 5. The two cells point along the row and clear it.
With two cells it is called a pointing pair, with three a pointing triple. The logic is the same. This is the first technique that removes candidates without placing a digit, so it is the point where pencil marks start to matter.
- Choose a box and a digit that is not placed in it yet.
- Mark the cells of the box where that digit could go.
- If they all share one row or one column, remove the digit from every other cell of that line outside the box.
- Check what the removal unlocks: often a hidden single appears straight away.
A real example
The blue candidates are the only places for the digit inside the highlighted box, and they line up. The red candidate further along the line is removed.
How to spot them
Look at boxes where a digit has only two or three possible cells. Rows and columns of filled cells inside a box make this likely: if a box has a full row, the remaining candidates are squeezed into the other two rows, and sometimes into one. Scanning digit by digit, the way you look for hidden singles, finds pointing pairs along the way.
Common mistakes
- Removing the digit from the box itself. Pointing removes it from the line outside the box.
- Using it when the candidates are not all on one line. One stray candidate elsewhere in the box breaks the pattern.
- Forgetting to follow up. The removal is only worth making for what it unlocks.
The mirror image of this technique is box/line reduction, where a line locks a digit into a box.
Questions
What is a pointing pair in Sudoku?
A pointing pair is two cells in one box, on the same row or column, that are the only places a digit can go in that box. The digit can then be removed from the rest of that row or column.
Which puzzles need pointing pairs?
Puzzles rated expert usually need at least one pointing pair or box/line reduction. Easy, medium and hard puzzles can be solved without them.