Hidden single
A hidden single is the single most valuable technique to learn after scanning. The square holding it does not look special — it may still show four or five candidates — and that is precisely why so many solvers stall on puzzles that are full of them.
The idea
Look at a unit — one row, column or box — and pick a digit. If there is exactly one square in that unit which could accept it, the digit goes there. It does not matter what else that square could have been.
The deduction is about the unit, not the square. That is the mental switch that has to happen, and it is the difference between a naked single and a hidden one. A naked single asks "what is left for this square?". A hidden single asks "where is there left for this digit?".
The same technique is sometimes called the last remaining cell, because what you end up with is one surviving square for the digit. That name describes the outcome; hidden single describes why the square is easy to miss, which is the part worth remembering.
A worked example
Column 3 is missing several digits. Follow the 6.
Column 3 has four empty squares. Rows 1, 2 and 7 each already contain a 6 somewhere else, which strikes the 6 out of r1c3, r2c3 and r7c3. Only r4c3 can still take it, so the 6 goes there.
Look at r4c3 again: it shows four candidates. Nothing about the square says "6". If you were hunting for naked singles you would have skipped straight past it.
How to scan for them
Take one unit and run the digits 1 to 9 through it, asking each time how many squares could hold that digit. It is slower than scanning, but it is mechanical, and on a medium or hard puzzle it almost always finds something.
If you keep notes, there is a faster version: look down a unit for a digit that appears in exactly one square's pencil marks. That is a hidden single, and it reads off the page once you know to look for it.
When you will need it
Hidden singles are the main thing separating medium from easy. An easy puzzle can generally be finished by scanning alone; a medium one is built so that scanning runs out and this is the move that reopens it.
Common mistakes
The commonest is checking only boxes. Hidden singles in rows and columns are just as frequent and far less often spotted, because the box is the unit people picture most readily. When stuck, sweep the rows and columns specifically.
The second is finding one and not acting on the consequences. A hidden single often unlocks a second one in a crossing unit immediately — place it, then re-check the row, column and box it sits in before moving on.
Common questions
What is a hidden single in Sudoku?
A hidden single is a digit with exactly one possible square left in a row, column or box. That square may still be showing two or three other candidates, which is what hides it, but the digit has nowhere else in the unit to go, so it is placed there.
How do I find hidden singles in Sudoku?
Work one digit and one unit at a time instead of one square at a time. Ask where this digit can still go in this box, then in this row, then in this column. Counting the possible homes for a digit is the entire scan, and a count of one is a placement.
Why is it called a hidden single?
Because the square holding it looks unremarkable. It still shows several candidates, so a scan hunting for squares that are down to one option passes straight over it. The digit is hidden behind the square's other candidates rather than behind any complexity in the logic.
Are hidden singles harder than naked singles?
Harder to see, not harder to justify. The deduction is a single step either way. The difference is that a naked single announces itself in the candidate list while a hidden single only shows up if you go looking for it digit by digit.
Where to go next
The next technique in the order is notes — Writing each square's remaining candidates, and the deductions that only appear once you do.
Coming to this cold? The step before it is naked single, and this technique is usually the one you reach for when that stops opening squares.
All nine techniques: the techniques index. New to the rules? Start here. Ready to use it? Open a board. Run a puzzle site? Embed this board.
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