Pointing: a digit locked to one line
Updated
A digit inside one box has lined itself up. Two homes, maybe three, and they all sit in the same row. Whatever the box decides later, that row has already spent the digit. You can take it off the rest of the row. Usually you place nothing. The lists just get shorter, and you go back to singles.
Run the same idea from the line instead of the box, and you have box-line reduction. Some people call that claiming. A digit along a row lives only inside one box, so the rest of the box loses it.
Both checks are Medium, with pairs. Triples come next on the ladder and have no page of their own. Their definition is on easy, medium, hard and expert Sudoku.
When to use it
Singles are done, and one digit keeps drawing a neat line. Notes help, because you are following one digit across a box and a row. Follow the 7s on the first board. The two cells inside the box show their full lists. Outside it, the marks show only the 7s you can remove. On the second board, the 4s below the row are the removals, not full lists.
Pointing
Look inside one box. If a digit’s homes there all share a row, the digit cannot appear in that row outside the box.
In the top-left box, follow 7. A 7 is already placed at r4c1, so column 1 is closed to 7, including r1c1, r2c1, and r3c1. Inside the box, r2c2, r2c3, r3c2, and r3c3 are filled. The only cells left that allow 7 are r1c2 and r1c3. Both sit in row 1. Their full lists are 5, 6, 7, 8, and 9. This is not a single and not a pair. It is a lock on the digit.
So 7 leaves row 1 outside the box: r1c4 through r1c9. The 7s marked on those cells only show the digit this step deletes. Those cells have other candidates too. The two cells inside the box can still be 7, or anything else on their lists. You do not choose between them.
7 in the top-left box sits only in row 1. Marks outside the box show 7 alone, not the full list. Those 7s are deleted.
A column works the same way. If the homes in the box share a column, delete the digit from that column outside the box. It is the row case, turned.
Box-line reduction
Start from the line. If a digit in a row has all of its homes inside one box, the rest of that box cannot be the digit.
On the next board, row 1 is open at columns 1, 2, 3, and 4. Column 4 already holds a 4 at r4c4, so r1c4 cannot be 4. The other open cells, r1c1, r1c2, and r1c3, are all in the top-left box, and each still allows 4. Their full lists are 1, 4, 8, and 9. Digit 4 in this row lives only in that box.
Delete 4 from the other six cells of the box: row 2 and row 3, columns 1 to 3. The step still places nothing. r1c1 still has all four candidates: 1, 4, 8, and 9. Only the six cells below it lose 4. The 4s marked below the row are the removals, not those cells’ full lists.
4 in row 1 sits only in the top-left box. The 4s below the row are the candidates this step removes.
A column locked into one box is the same rule. Delete the digit from that box, outside the column.
The step
- Pick a digit, not a cell that looks likely.
- Pointing: if its homes in one box share a row or a column, delete it from the rest of that line.
- Box-line: if its homes in one row or column share a box, delete it from the rest of that box.
- Go back to singles. A cell left with one digit is a naked single on the next pass.
Easy to misread
Two homes in a box are not enough. They must share a row or a column. If they share neither, there is no pointing deletion. I have cleaned a row before the homes lined up. The digit was still free, and I had to put the candidates back.
Do not fill a cell because the digit looks ready. Pointing and box-line only remove candidates. Inside the lock, the digit still has more than one home.
Next
Next time a digit draws a straight line through a box, try taking it off the rest of that line before you hunt a harder shape. The next technique page is X-Wing. Between pointing and X-Wing, the ladder uses triples. There is no separate article. The definition is on the difficulty page linked above.