Hidden single: One digit, one possible place
Learn to find the only place for a digit in a row, column or box, even when the cell has several pencil marks.
Ask a different question
A naked single asks which digit can fit in one cell. A hidden single changes the focus and asks where one digit can fit within a unit. Every row, column and box needs one occurrence of each digit from 1 to 9. If a digit can occupy only one of its empty cells, that position is settled. The cell may show several pencil marks, which is why the answer is hidden among them. The proof comes from comparing all possible positions for that digit in the unit you are inspecting.
A row example
In a local candidate situation, row 2 is missing {2, 5, 7, 9}. Its four empty cells have these complete lists: r2c1 {2, 5}, r2c3 {2, 7}, r2c6 {2, 5, 9} and r2c8 {5, 7}. The digit 9 appears only in r2c6. Therefore r2c6 = 9, even though that cell also contained the pencil marks 2 and 5. None of the other three empty cells in the row can take 9. Their exclusions, checked against their columns and boxes, establish the placement.
Search inside boxes too
Exactly the same reasoning works in a 3 × 3 box. Choose a digit that is still missing and inspect the empty cells. Existing copies of that digit in rows and columns crossing the box can rule out positions. When only one position remains, place the digit there. You do not need a full set of pencil marks to find this move, but you do need to check every relevant position. If two positions remain possible, keep both. A cell looking less crowded than another does not turn a visual preference into a deduction.
Avoid a false hidden single
Incomplete pencil marks can create the appearance of a unique position. If you wrote a small 6 in just one cell but forgot to inspect another, you have not established a placement yet. Before entering 6, ask why it cannot go in every other empty cell in that unit. Also check that 6 is not already placed somewhere in the unit. After a valid move, clear the other candidates from the solved cell and update related units. This short check keeps the reasoning tied to the grid rather than relying blindly on your notes.
Check your understanding
A column needs {1, 4, 6}. Its three empty cells have the complete lists {1, 4}, {1, 4, 6} and {1, 4}. Only the second cell allows 6, so that cell must be 6. You do not yet know the order of 1 and 4 in the other two cells. If the final list changed to {1, 4, 6}, there would be two possible places for 6 and this technique would no longer settle it. Compare this with a naked single: The certainty comes from a digit having one location, rather than a cell having one candidate.
8 cannot go in the other five cells of this row. Where must it go?
r2c1 {1,3} · r2c2 {3,7} · r2c3 {1,7} · r2c4 {2,8}
Now try it on the grid.
Return to an easy puzzle and look for a chance to use what you’ve learned.
Practise with a Sudoku