The first two techniques both end with you writing a number in a square. This one doesn't, and that's the thing to get used to.
A pointing pair doesn't solve anything. It rules something out — somewhere else on the board, often a long way from where you were looking. Then the techniques you already know finish the job.
That sounds like a downgrade. It isn't. Most of the work in a hard puzzle is clearing possibilities away until a single falls out, and this is the first tool that does the clearing.
Two homes, one line
Here's the whole idea, and it fits in a sentence.
If every place a number could go in one box sits on the same row, then that number is somewhere on that row — you don't know which square yet, but you know the row. And a row can only hold one of each number. So that number can't be anywhere else on that row, including the parts of the row outside the box.
Columns work the same way, turned ninety degrees. If every place a number could go in a box sits in the same column, that number is somewhere in that column, and it's cleared from the rest of the column above and below the box. Rows and columns are the two halves of this technique and neither is the special case — the worked example below happens to be a row, and the exercise at the end is two columns.
Either way you've gone from "I don't know where this number goes" to "I don't know where it goes, but I know enough to cross it off five other squares." That's the trade.
Look at the box in the top-left corner. It holds 5, 3, 6, 9 and 8, so four squares are empty and four numbers still need homes.
Take the 7, and ask the question from the last piece: where in this box can it go?
Positions below are given inside the box — "the box's top row" is the box's own top row, not the grid's.
- The box's top row, right-hand square. Its row already has a 7, over in the middle of the grid. Out.
- The box's bottom row, left-hand square. Its column already has a 7, further down. Out.
- The box's middle row, both empty squares. Neither their rows nor their columns have a 7. Both survive.
So the 7 has two homes, and no way to choose between them.
There's the 7, twice, and nowhere else in the box.
Now stop trying to place it, and read what you've got. Both of those squares sit on the box's middle row — which is the second row of the grid. Whichever one takes the 7, the 7 for this box is on that row.
That's the pointing pair. Two candidates, one line, pointing.
What it buys you
That row runs the full width of the grid, and it now has a 7 committed to its left-hand end. Everywhere else along it, the 7 is dead.
Here is the whole of that row with its candidates filled in — the two squares from the box on the left, and the three still-empty squares at the right-hand end.
Look at the right-hand end. Two of those three squares are carrying a 7 — the first and the third. Until a moment ago you had no reason to doubt them.
Now you do. The 7 for the top-left box lives somewhere on this row, and a row holds one 7. So neither of those squares can be it.
Cross them off.
That's the technique, done. Nothing was placed and nothing was solved — but two squares got smaller, and squares getting smaller is how naked singles are born.
You didn't find out where the 7 goes. You found out where it doesn't, and that turned out to be worth more.
The jargon, deflated
Pointing pair. For once the name is doing its job: two candidates, pointing along a line. If three squares in the box share a line instead of two, it's a pointing triple and it works identically — the count was never the point, the shared line is.
You'll also meet the mirror image, where a row's candidates for a number all sit inside one box, so the number gets cleared from the rest of that box. Same trick, read the other way round. It's called box-line reduction, and if you can do this one you can already do that one.
Both belong to a family worth naming, because it changes what you're looking for: these are techniques that narrow candidates rather than place numbers. Every technique past this point is one of those. If you've been waiting for each move to produce a digit, this is where that expectation has to go, and losing it is most of what people mean by getting better at Sudoku.
When to reach for it
Pointing pairs are not a scanning technique. You won't spot them by staring at a grid — you find them when you've written candidates down and a box has a number with exactly two or three homes.
So the honest advice is: use this one after the first two have stopped paying. Work naked and hidden singles until nothing falls out, and only then start reading boxes for numbers with two homes on a line. Reaching for it first is a lot of work for a payoff you could have had faster.
Which is worth being straight about, since we've been on the same grid for three articles: this puzzle never stops paying. It's an easy board and singles alone will finish it. The pointing pair above is real — that 7 genuinely has two homes and genuinely clears two squares — but you're seeing the technique on a board you already know rather than on one that requires it. You'll meet the version that requires it on a Hard puzzle, and it will look exactly like this.
One more thing worth knowing, because it saves wasted effort. A pointing pair is only useful if the line leaves the box with something on it worth killing. If the rest of that row is already full, or none of the remaining squares wanted that number anyway, you've found a real pointing pair that buys you nothing. That's not a mistake, it's just a dry one. Move on.
Now find one yourself
Same grid, still at its starting position — this is board one again, unchanged, so nothing from the worked example has been carried over.
Numbers for squares from here on: rows count from the top, columns from the left, so row 4, column 7 is the seventh square along on the fourth row down.
The box to work on is the one on the right-hand edge, level with the middle of the grid — rows four to six, columns seven to nine. It holds 3, 1 and 6 down its right-hand column, and six squares are empty.
There are two pointing pairs in that box, and either one counts. Both point down a column rather than along a row, which is the only hint you should need.
Work it the way the worked example went: pick a number the box still needs, find every square in the box that could take it, and check whether they all share a line.
Expect to try more than one number. That box is missing six numbers and only two of them are pointing pairs — three lead nowhere in particular, and one turns out to be a hidden single instead. Drawing a blank on a number is the search working, not failing. You're ruling out a number, which is the same thing this technique does to squares.
Both answers, and a third thing in the same box — open when you've had a go
| Number | Homes in the box | Points down | Clears it from |
|---|---|---|---|
| 7 | row 4 column 7, row 5 column 7 | column 7 | row 2 column 7, row 3 column 7 |
| 2 | row 4 column 8, row 5 column 8 | column 8 | row 1 column 8, row 2 column 8 |
Why the 7 is confined. The box's right-hand column is already full, so only six squares are in play. Row 6 has a 7 at the far left of the grid, which kills both squares on the box's bottom row. Column 8 has a 7 down at the bottom of the grid, which kills the other two. What survives is column 7, rows 4 and 5.
Why the 2 is confined. Column 7 has a 2 just below the box, which kills all three of the box's squares in that column. Row 6 has a 2 in the middle of the grid, which accounts for the last one on the bottom row. The survivors are column 8, rows 4 and 5.
The third thing. The 8 in that box has only one home — row 6, column 7. One home isn't a pointing pair, it's a hidden single from the last piece, and you can simply place it. Worth noticing that all three techniques so far are sitting in the same nine squares. That's normal. Puzzles don't hand you one technique at a time, and part of getting quick is recognising which one a situation is asking for.
Where you are now
Three techniques, and they stack:
- Naked single — this square has one number left. Places a number.
- Hidden single — this number has one square left in a region. Places a number.
- Pointing pair — this number's squares in a box share a line, so it's cleared from the rest of that line. Places nothing, and makes the first two more likely.
That third one is the shape of everything ahead. The techniques get longer names and cover more squares, but they all do the same job: take possibilities away until something has nowhere left to hide.
Run the first two until they stall. Then read a box, clear a line, and go back to the first two — which will usually have something for you that they didn't a minute ago.
Earlier in this series: naked singles and hidden singles. The whole ladder is laid out in Sudoku techniques, in the order worth learning them.