Hidden single: the only place a digit can go

What is a hidden single?

Every row, column and box must contain each digit from 1 to 9 exactly once. So for any digit that is still missing from a unit, there has to be a cell in that unit where it goes. If all the other empty cells of the unit are blocked for that digit, the one remaining cell must hold it.

That digit is a hidden single. It is “hidden” because the cell itself may look open: it can still have three or four candidates. You only see the answer when you compare the cells of the unit with each other, focusing on one digit at a time.

Hidden single vs naked single

A naked single starts from a cell and eliminates digits until one is left. A hidden single starts from a digit and eliminates cells until one is left. Both are pure logic and both are enough to solve Quietdoku’s Easy puzzles, but they find different things. A cell can hold a hidden single while still showing four candidates, so if you only ever look for naked singles, you will miss many easy placements.

How to scan for hidden singles

Pick one digit, say 4, and find every 4 already on the board. Each placed 4 blocks its whole row and whole column. Now look at the boxes that do not contain a 4 yet. Inside each such box, cross out the cells that sit in a blocked row or column, and the cells that are already filled.

If exactly one cell of the box survives, you have found a hidden single. Players often call this cross-hatching, because you are mentally drawing lines through rows and columns. It is fastest on digits that already appear many times, since each copy blocks more cells.

Then repeat with the next digit, and do the same for rows and columns, not only boxes. A digit can be missing from a row and have only one legal cell in it, just as in a box. When you use pencil marks, a hidden single is a candidate that appears only once within a unit.

Worked example

Look at the middle-left box of the example board, box 4, which covers rows 4 to 6 and columns 1 to 3. It has no 4 yet, and five empty cells: R4C1, R5C1, R5C3, R6C1 and R6C2 (row 6, column 2).

The highlighted 4 in R2C1 sits in column 1, so none of R4C1, R5C1 or R6C1 can be 4. The highlighted 4 in R5C6 sits in row 5, so R5C3 cannot be 4 either. That leaves only R6C2, so R6C2 must be 4, shown in gold.

Now look at R6C2 on its own: its row, column and box still allow 1, 3, 4 and 5. From the cell’s point of view nothing is decided, which is exactly why this placement is invisible to a naked single search. The two given 4s, both outside the box, do all the work.

Common mistakes

Forgetting that filled cells are also unavailable. When you count the cells left for a digit in a box, only empty cells count. In the example, box 4 has four givens, so there were only five cells to rule out, not nine.

Scanning only boxes. Rows and columns produce hidden singles too, especially late in a puzzle when a row has only three or four gaps. Make it a habit to check the most crowded rows and columns for each missing digit.

Confusing “only candidate” with “only place”. A hidden single does not mean the cell has one candidate; it means the digit has one cell. Placing a digit because a cell “looks likely” is guessing. Place it only when every other cell in the unit is truly blocked.

When to use it and what comes next

On easy puzzles, a good rhythm is to sweep digits 1 to 9 for hidden singles, fill what you find, then check for naked singles around each new digit. Repeat until the grid is full.

When hidden and naked singles both run dry, you have reached medium territory. The next step is to write pencil marks and look for locked candidates, where a digit is confined to one row or column inside a box. Removing those candidates usually uncovers new hidden singles. If you are stuck, a Quietdoku hint points to the next step and names the technique.