Hidden Single Walkthrough
A Hidden Single is a digit that can legally go in only one cell of a row, column, or box, even though that cell still shows other candidates. The digit is forced into that single spot.
Below are 3 positions from real puzzles, each captured when the solver first needs this move. Find the pattern on each before-board yourself, then read the notes and check the after-board, where removed candidates are struck out in red and solved cells shown in green.
Example 1: There is a Hidden Single in Row 1
Row 1 is down to three open cells. Two of them, r1c1 and r1c4, show {6,8}, and r1c2 shows {5,6,8}. If you read cells, r1c2 looks like the least settled of the three. If you read digits, it is the most settled: the row still needs a 5, and r1c2 is the only cell that lists one. So 5 goes in r1c2. What remains is a matched {6,8} pair in r1c1 and r1c4, and the row will be finished as soon as either cell is decided from its column.
Example 2: There is a Hidden Single in Row 2
Here the trap is that every open cell in row 2 shows exactly two candidates: r2c3 {4,8}, r2c6 {7,8} and r2c7 {4,8}. A solver looking for Naked Singles finds nothing. Count digits instead. The row is missing 4, 7 and 8. The 4 and the 8 each have two possible cells, but 7 appears only in r2c6, so r2c6 is 7. With that placed, the other two cells hold the 4 and the 8 in some order that row 2 alone cannot settle.
Example 3: There is a Hidden Single in Column 7
This one runs down a column rather than along a row. Column 7 has four open cells, r1c7 {3,7}, r3c7 {3,9}, r6c7 {3,8,9} and r7c7 {3,8}, and needs 3, 7, 8 and 9. The 3 could still go in any of the four, but the 7 is listed only at the top, so r1c7 takes it. Reading the column top to bottom and tallying how often each digit appears is the whole method, and a digit that turns up once is placed.
Why the deduction is valid
A Hidden Single reverses the question. Instead of asking what can go in this cell, you ask where this digit can go in this unit. Every row, column and box must contain all nine digits exactly once, so if a digit has been squeezed out of eight cells of a unit, the ninth cell is forced — regardless of how many other candidates that cell still shows. The candidate is "hidden" precisely because the cell looks undecided.
How to spot a Hidden Single on your own board
- Cross-hatch one digit at a time. Pick a digit, find every box that does not yet contain it, and draw imaginary lines through the rows and columns that already do. Boxes where only one cell survives are your placements.
- Prioritise digits that already appear five or six times on the grid. The more copies placed, the more lines they project, and the more likely they have squeezed themselves into a corner somewhere.
- Boxes are usually more productive than rows or columns, because a box is constrained by three rows and three columns at once.
Common mistakes
- Dismissing a cell because it has several candidates. That is exactly the condition that makes the single hidden — a cell with four pencil marks can still be the only home for a digit in its box.
- Cross-hatching a digit once and never returning to it. Every subsequent placement changes the picture, so a digit that yielded nothing on the first pass often yields immediately on the third.
What to do next
Hidden Singles and Naked Singles feed each other: the digit you just placed removes candidates elsewhere, frequently exposing a Naked Single a cell or two away. Alternate between the two questions — "what fits here" and "where does this go" — until neither produces anything.