Hidden single: scanning a row, column, or box

Sometimes the cell will not tell you its digit. The digit will. You pick a 4, or a 6, or a 3, and you walk it along one row, one column, or one box until only one chair is left. That is a hidden single. The cell that receives it may still be holding a long list. It never announced itself.

Start with a box, then try a row and a column. Each time, you’re asking the same question: where can this digit still go?

When to use it

Look for it after a naked single, or in between. Easy puzzles on Calmtile stop at these two. Notes help, and you can do without them. With notes, the digit shows up in only one list inside the house you are scanning.

Where to look

One digit. One house. Cross out every cell in that house that is already filled, and every empty cell that can see the digit somewhere else. One cell left, and you place it there.

In a box

The first board is hunting 4 in the top-left box. r1c2 and r1c3 are already filled. Row 2 has a 4 in the top-middle box, at r2c5, so the top-left box cannot put 4 anywhere in row 2. Row 3 has a 4 at r3c8, so row 3 inside this box is closed too. The only chair left is r1c1.

r1c1 can still be 3, 4, 5, 6, 7, 8, or 9. It is not a naked single. You found 4 by asking where 4 can sit, not by asking what the cell wants to be.

In the top-left box, 4 can sit only in r1c1. The cell still has other candidates.

3456789	1	2
				4
							4

In a row

Same test, turned sideways. Digit 6 has been placed once in every column except column 5, and none of those sixes sits in row 5 or in the center box. Every cell of row 5 except r5c5 shares a column with a 6. r5c5 does not see a 6 in its row, its column, or its box. So 6 belongs there, and nowhere else in the row.

The cell itself still allows 1 through 9. The 6 is hiding in a full list. Staring at the cell will not show it. Scanning the row for 6 will.

Row 5 can put 6 only in r5c5. The cell's own list is still every digit.

6
			6
						6
	6
				123456789
							6
		6
					6
								6

In a column

Column 8, digit 3. Each of the other eight rows already holds a 3, all of them outside this column and outside the box around r4c8. Those threes close every other cell of the column. Row 4 has no 3, column 8 has no 3, and the box has no 3. r4c8 can be 3, and it is the only place in the column. Its own list is still 1 through 9.

Column 8 can put 3 only in r4c8.

3
			3
						3
							123456789
		3
				3
	3
					3
								3

The step

1. Pick a digit, then a house. Start with a box, then a row, then a column. That order is easier not to miss.
2. Cross out every cell in the house that cannot hold it.
3. One cell left: place the digit.
4. Two or more left: leave it, and try another digit or another house.

Naked single and hidden single

	Naked single	Hidden single
You look at	one cell	one digit
The question	What can this cell be?	Where can this digit go?
The cell’s list	one digit	may still be long

Both steps place a digit. Neither one is a note, and notes are not a grade.

Easy to misread

Do not wait for the cell to look lonely. In all three examples the cell you fill still has other candidates. The question is how many homes the digit has left in this one house.

Do not stop after the box, either. A digit with two homes in the box may already have one home in a row or a column. Walk all three before you decide it is stuck.

Next

When the scans leave empty cells, you can write the leftovers down. That page is notes. You can also skip them. They are not a difficulty of their own.