Hidden singles in Sudoku: find the only place for a digit
A hidden single occurs when a digit has only one legal position within a Sudoku row, column or box. That cell may still have other candidates. Place the digit because the unit must contain it, and every other position in that unit is ruled out.
The worked example
Read coordinates from the top left: r = row, c = column. Small digits are candidates. Outlines identify the cells discussed in the caption.
Open this example in the solverView the exact 81-cell input
Read left to right across each row, then top to bottom. A 0 means a blank.
003056789056789123789023456234567891567891234891234567345678912678912345902345678Find the missing 2 in row 1
Row 1 contains 3, 5, 6, 7, 8 and 9, so it needs 1, 2 and 4. Its empty cells are r1c1, r1c2 and r1c4. Each has two basic candidates; there is no naked single among these three cells.
Every completed row must contain a 2. Both alternatives are excluded, so r1c2 = 2. The extra candidate 1 in that cell does not prevent the placement; the requirement to put a 2 somewhere in row 1 settles it.
| Empty cell | Candidates | Can it take 2? |
|---|---|---|
| r1c1 | 1, 4 | No: column 1 contains 2 at r4c1 |
| r1c2 | 1, 2 | Yes: no 2 in its row, column or box |
| r1c4 | 1, 4 | No: column 4 contains 2 at r6c4 |
A reliable scan uses a whole unit
Pick one missing digit and examine every empty cell of a single row, column or box. Keep the unit fixed while counting positions. A 2 that appears once in a few selected cells is not enough: an unchecked cell elsewhere in that same unit may still accept it.
Step 1. Choose a unit and a digit it is missing. Here, choose row 1 and digit 2.
Step 2. For each empty cell, check the other two units that constrain it.
Step 3. Count all legal positions. Exactly one position proves a hidden single; two or more do not.
Step 4. If there are no legal positions, investigate an inconsistency instead of placing the digit arbitrarily.
Step 5. After placing the digit, update affected notes and rescan for newly exposed singles.
What happened to the candidate 1?
Before the deduction, 1 passed the basic row, column and box checks at r1c2. Those checks are local. They did not establish that an entire solution could contain that 1.
If you put 1 there, neither r1c1 nor r1c4 could take the missing 2, so row 1 could never be completed. The hidden-single argument rules out that global dead end without trial and error. In the no-solution guide, the same wrong entry becomes a concrete diagnostic example.
A two-candidate cell is not automatically a pair
The notes {1, 2} in r1c2 describe one cell. They do not establish a naked pair: that requires two cells in a shared unit whose candidate sets together contain exactly the same two digits. Nor do they make the cell a 50–50 guess.
In this row, checking where the 2 can go is sufficient. Use the simplest complete proof available. You do not have to remove the 1 from every related cell or solve the rest of the board before committing to r1c2 = 2.
Check your understanding
Row 1 also needs a 4. Is 4 a hidden single in row 1 at the start?
Show the reasoning
No. Both r1c1 and r1c4 can currently contain 4. A hidden single needs exactly one legal position in the chosen unit. The fact that digit 2 has a unique position does not give digit 4 one.
About this example
This example was constructed for Sudoku Slate from a completed grid. Many givens are retained to make the specific deduction easy to inspect. Diagnostic examples are deliberately conflicting or ambiguous where stated; these are teaching positions, not difficulty-rated game puzzles.
Rules and terminology
- Nikoli: Sudoku rules
The standard row, column and 3 × 3 box rules used in these examples. The board and worked explanation on this page were created separately.
- Andrew Stuart: Naked Candidates
Established terminology for naked singles and their relationship to hidden singles. The board and worked explanation on this page were created separately.