Lesson 4 of 9
Hidden single
The only square in a row, column or box that can hold a digit — even when it still shows other notes.
What this grid does
- Starting digits
- 24 of 81
- Deductions to solve
- 60
- Uses of Hidden single
- 2
- Squares placed by scanning
- 57
- First needed at
- deduction 8, in row 9 (R9C1, R9C2, R9C3, R9C4, R9C5, R9C6, R9C7, R9C8 and R9C9, on the 2)
- Also calls for
- last free cell, cross-hatching, naked single and naked pairs
Measured on this grid by the same solver the hint button uses — how these puzzles are chosen.
Why this one is worth drilling
About 64 in every 100 puzzles need it, so you meet it constantly and can learn it simply by playing. That figure is measured rather than guessed: 64% of solvable 24-clue grids over 300 digs.
This is the first technique people genuinely stall on, because the square that takes the digit still shows two or three other candidates. Nothing about the square announces it. The signal is in the unit, and if you are looking at squares you will not see it however long you stare.
Where it sits in the nine
Fourth, and the genuine step up. The three before it argue from what a square can hold; this one argues from where a digit can go, and that inversion is the single most useful idea in Sudoku. It is also the last technique that places digits directly — from lesson five on, deductions stop filling squares and start erasing candidates.
Working it
Change the question. Instead of asking what goes in a square, take one unit and one digit it is missing, and ask where that digit can still go. Work through the digits a unit is missing in order. It feels slower than scanning and finds things scanning cannot. Boxes first, then rows and columns. A box constrains a digit from three directions at once, so hidden singles surface there far more often, and working boxes first means fewer wasted passes. When a box yields nothing for any missing digit, that is the signal to widen to its rows and columns rather than to start writing candidates everywhere.
The full explanation of hidden single covers the reasoning with diagrams.
Last reviewed