Lesson 7 of 7 · Pair technique
Pointing pairs: when a box and a line agree
The guide and all sudoku lessons
A box and a line (a row or a column) overlap in three squares. Pointing pairs use that overlap. If a digit's only possible squares inside a box all lie on the same row, then wherever the digit ends up in that box, it is on that row. So it cannot be anywhere else on the row, outside the box. Clear it from there.
The same idea runs the other way. If a digit's only possible squares on a row all lie inside one box, the digit must land in that box on that row, so it cannot be anywhere else in the box. Some guides call this claiming, or box-line reduction.
Like a naked pair, this technique removes candidates rather than placing a digit. It is worth looking for whenever a digit's marks inside a box, or along a line, line up.
Example 1: From a box to a row
Step 1 of 4
Where can the 5 go in the bottom-left box? Read the marks of its four empty squares.
Read the bottom-left box for the 5. Only two of its four empty squares can take it, and both sit in row 8; the squares in rows 7 and 9 have no 5 among their marks.
Wherever the 5 ends up in that box, it is in row 8. So no other square in row 8 can be a 5. The ringed square, in column 7, was showing 5 and 8: the 5 goes, and the 8 lands. No single on this board reaches that 8; the box told you something about the row.
Example 2: From a row to a box
Step 1 of 4
Where can the 4 go in row 4? Read the marks of its three empty squares.
Now the other direction. Row 4 has three empty squares, and the 4 can only go in two of them, both inside the middle-right box.
Whichever of the two takes the 4, it lands inside that box, so no other square of the box can be a 4. The ringed square, at row 5, column 9, was showing 3 and 4. Clear the 4 and it is a 3.
Try it yourself
A new board, and the same idea. Get it wrong and the board tells you why.
The marks in the top-middle box and the ringed square are filled in, and no single is left on the board. What goes in the ringed square?
Pick the digit for the ringed square.
How to spot it faster
- For each box, look at one digit's marks. If they all sit in one row or one column, check the rest of that line for the same digit.
- For each row and column, do the reverse: if a digit's marks all sit in one box, check the rest of that box.
- These come up most often in boxes where only two or three squares can take a digit.
- After clearing, check the square you edited for a single.
Common mistakes
Clearing inside the overlap
Only remove the digit from squares outside the overlap: the rest of the line for a pointing pair, the rest of the box for claiming. The squares that line up keep their marks.
A third square you missed
Every square in the box that can take the digit must lie on the line. One stray mark elsewhere in the box, and the conclusion does not hold.
Mixing up the directions
From a box to a line, clear the line. From a line to a box, clear the box. The reasoning is the same; what you clear is not.
Questions
Try it
On a hard board, pick a digit and walk the boxes: wherever its marks line up, check the rest of that line. Then walk the rows and columns the other way.
Play solo on a hard 9×9