Hidden Singles

Hidden singles are the second technique most solvers learn, and they unlock more of the grid than naked singles do. If you can find naked singles in your sleep but still feel stuck halfway through a puzzle, hidden singles are usually the answer.

The definition

A hidden single is a digit that can only go in one cell within a particular row, column, or 3×3 box. even though that cell might have several other candidates.

That last part is the key difference from naked singles. A naked single is about the cell: only one digit fits there. A hidden single is about the digit: it only fits in one cell of that row, column, or box.

Why it's called "hidden"

Because the cell where the digit goes doesn't look special. It might accept 3, 5, and 7 in terms of row/column/box constraints, so it doesn't show up as a naked single. But across the whole row, 5 happens to fit nowhere else. The 5 is "hidden" among the cell's other candidates.

Most solvers miss them because they scan cell by cell, asking "what fits here?" To find hidden singles you have to ask the opposite: "where can this digit go?"

How to find them

Pick a digit. Walk through the nine rows and ask, for this digit, which cells could it go in? Cross out the cells that already have the digit elsewhere in their column or box. If a row ends up with only one possible cell, you've found a hidden single.

Do the same for columns. Then for the nine boxes. Most hidden singles live in boxes, because boxes have the most overlapping constraints.

After a placement, the digit you just placed has new positions ruled out in its row, column, and box, so re-scan that digit immediately. You'll often find a second hidden single right next door.

A worked example

Suppose the top-left 3×3 box has three empty cells: r1c1, r2c2, and r3c3. You want to know where 5 goes in that box.

Check each candidate cell. Does r1c1's row already have a 5? Yes, let's say there's a 5 in r1c8. So r1c1 can't be a 5. Does r2c2's column have a 5? Yes, in r6c2. So r2c2 can't be a 5 either. That leaves r3c3. The 5 in the top-left box has to go in r3c3, even though r3c3 might also accept 2 and 8 as far as its own row, column, and box constraints are concerned. The 5 is hidden in that cell.

Place it. Now the column and box are tighter, and another digit's candidate set just shrank elsewhere. Keep scanning.

When to look for them

Hidden singles thrive after a few placements have happened. Right at the start of a puzzle there are too many empty cells; later on, the constraints tighten and hidden singles appear.

A good habit: after every two or three placements, pause and walk through the digits one at a time. Pick the digit that's been placed the most so far. say, the 4 that already appears in seven of the nine rows. With only two rows left to place it in, the 4 is heavily constrained, and a hidden single is almost guaranteed.

Common mistakes

Scanning by cell instead of by digit. Scanning "what fits here?" finds naked singles. To find hidden singles you have to flip it: "where can this digit go?" Different question, different scanning pattern.

Forgetting to re-scan after a placement. A placement can create a hidden single in any unit that already had partial coverage of that digit. Re-scan, especially the boxes that share a row or column with the placed cell.

Confusing them with naked singles. If you find a cell where a single digit is forced, it's a naked single. If you find a digit that's forced into a single cell within a row, column, or box, it's a hidden single. The placement is the same; the way you spotted it is different. The distinction matters because hidden singles need a different scan.

What hidden singles let you skip

Most medium puzzles can be solved with only naked and hidden singles . no pencil marks needed. If you're laying down pencil marks on a medium sudoku, you've probably missed a hidden single. Stop and scan each digit before reaching for the notes.

On hard and above, you'll still need pencil marks eventually, but clearing out the hidden singles first means fewer candidates to track. Always exhaust singles before any other technique.

Practise it

Play easy or medium sudoku and force yourself to scan by digit instead of by cell. It feels awkward for a few games. Stick with it. After a week you'll spot hidden singles in two or three seconds.

Once hidden singles are automatic, the natural next move is to learn pencil marks, and from there naked pairs. Each technique builds on the last.

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Tip / note / warning callouts

Pull quote

"If you've ever wondered why hard sudokus feel impossible, the answer is usually a hidden single you missed in a box you'd already scanned."

Step list

1. 1
   Pick a digit

   Choose one number from 1 to 9 to focus on. The most-placed digit so far is usually the best starting point.
2. 2
   Walk the units

   Check each row, column, and box for that digit. Mark cells where it could still go.
3. 3
   Find the lonely one

   If a unit has only one open candidate cell, that's where the digit goes.

Comparison table

Key-value list

Tier

Beginner

Found in

Rows, columns, boxes

Pencil marks

Not required

Typical use

After every placement, re-scan affected units

Big stat

Checklist

• ✓Scan the digit through every row before moving on
• ✓Re-scan boxes after each placement
• ✓Don't reach for pencil marks while singles still exist
• ✓Track which digits you've already scanned this round

Code / notation block

r5c3 = 7    → place 7 at row 5, column 3
r5c3 ≠ 7    → eliminate 7 from r5c3
b4 hidden 7 → 7 is forced into one cell of box 4

Two-column layout

Strategy illustration gallery

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