Hidden singles

What a hidden single is

A hidden single is a digit that has exactly one place left to go in a row, a column or a 3×3 box — even though the cell it belongs in still looks like it could hold several different digits.

That last part is the whole point, and it is where the name comes from. A naked single is a cell with one candidate left: obvious, and most solvers spot it without trying. A hidden single is invisible from the cell’s point of view. You only find it by turning the question around.

The question that finds them

Beginners ask “what can go in this cell?” and work cell by cell. That finds naked singles and nothing else. The productive question is the other one:

“Where can this digit go in this unit?”

Pick a digit, pick a row, column or box, and check each empty cell in it. If eight of the nine are blocked — by that digit already appearing in their column, their row or their box — the ninth is forced, whatever else it might have held.

How to hunt them efficiently

Do not sweep at random. Work digit by digit, and start with the digits that already appear most often on the board — a digit placed six times has only three homes left, and its constraints reach across most of the grid.

For each of those digits, look at the boxes it is missing from. Cross off the rows and columns that already contain it, and see what is left. Most hidden singles fall out of that one pass, and it is fast enough to be worth doing in a timed match where marking every candidate is not.

Why this is the technique that matters most

Hidden singles and basic scanning solve the overwhelming majority of easy and medium puzzles outright. Everything further down the list — naked pairs, X-Wing, Swordfish — exists for the boards where this one has already been exhausted.

If you learn exactly one technique beyond the rules, learn this one. It is also the fastest to apply, which makes it the technique that decides races.