Pointing: when a box points down a line
If a digit’s places in a box all sit in one row, that row gets its digit from the box. The rest of the row can’t have it.
How it works
Look at one digit and one box. The box needs that digit somewhere. Sometimes every place it could go in the box is in the same row.
Then the box’s digit is in that row. And the row can only have one of that digit, so it is the box’s. No other cell in the row, outside the box, can be that digit.
This is pointing. The box “points” along the row and clears it. Two “exactly one” rules, the box’s and the row’s, meet in the same cells.
The other direction
It works from the line’s side too. If all of a row’s places for a digit sit inside one box, the row’s digit is in that box. So the box’s other cells can’t have it.
Solvers call this box/line reduction or claiming. It is the same two rules, read the other way.
Why it is valid
Let the box’s 1 be in cell X. X is in row 1. Now take any cell Z in row 1 outside the box. If Z were 1 too, row 1 would have two 1s. So Z is not 1. The argument never needs to know which cell X is.
Worth memorizing
Look at one digit in one box.
Showing only that digit helps.
If its places line up, clear the rest of the line.
Row or column.
Two or three places in a line is enough.
You don’t need to know which one is right.
Practice
0 of 4 rightInside box 1, a 3 can only go in row 1. Which cells lose their 3?
Box 6’s places for 5 all sit in one line. Which?
Box 6 points its 1 along a row. Which cells lose a 1?
Where can 3 go in box 2? Which cell outside the box loses a 3?