Row Detective: The Only Home for a Digit

A row hidden single can be easy to miss when the target cell has several candidate marks. In this challenge, search for one required digit across a complete row. The fact that the destination cell has other possibilities does not matter if every other location for the required digit has been ruled out.

Read the row's missing digits and focus on the one named in the task. At each blank, inspect the crossing column and the box. If either already contains that digit, the location is unavailable. Make a small list of the rejected coordinates and their reasons.

The surviving cell may still have several legal candidates when considered alone. That does not weaken the row argument. The row must contain the target digit, and every alternative location has been excluded. Once the digit is placed, its other candidates disappear.

Try to state the proof without referring to the final answer: the required digit, the complete row search, and the single remaining coordinate. This makes the explanation checkable from the clues on the page. Then update the affected column and box. Use the full solution below only after your local reasoning is complete or when checking the rest of the solve.

5 . . | . . . | . 3 9
. 2 . | 1 5 8 | . . .
. . . | . 3 2 | . 5 .
------+-------+------
. 9 5 | 4 . 1 | 7 . .
. . 4 | 3 . . | . 2 5
6 7 3 | . 2 . | . 8 .
------+-------+------
1 . . | 2 . . | . . 8
. 5 . | 6 . . | 3 7 .
. 3 . | 8 9 5 | 4 . .

Your task

Where must 2 go in row 1? Check every blank in that unit and explain why the other locations fail.

5 8 1 | 7 4 6 | 2 3 9
3 2 9 | 1 5 8 | 6 4 7
4 6 7 | 9 3 2 | 8 5 1
------+-------+------
2 9 5 | 4 8 1 | 7 6 3
8 1 4 | 3 6 7 | 9 2 5
6 7 3 | 5 2 9 | 1 8 4
------+-------+------
1 4 6 | 2 7 3 | 5 9 8
9 5 8 | 6 1 4 | 3 7 2
7 3 2 | 8 9 5 | 4 1 6