A hidden single occurs when a missing digit can go in only one empty cell of a row, column or 3 × 3 box. The cell can still have several candidates. The placement is forced because the group must contain that digit once, and every other location is ruled out.
Hidden single versus naked single
A naked single asks, “What can go in this cell?” A hidden single asks, “Where can this digit go in this group?” A cell with notes 1 and 2 can be a hidden single for 1 if no other cell in its group allows 1. You can then place 1 and discard 2 from that cell.
The word “hidden” describes how the deduction can be concealed among other notes. You do not need an advanced pattern or a guess: you need a complete check of the possible locations for one digit.
An original worked example
In this teaching grid, row 1 is missing 1, 2 and 3. Dots mark empty cells; the shaded cell is row 1, column 1 (r1c1). This example comes from a valid completed grid and is separate from today’s Daily puzzle. Its purpose is to demonstrate one deduction, not a difficulty rating.
- List the row’s missing digits. Row 1 already has 4–9, so each blank starts with possibilities 1, 2 and 3.
- Check columns and the box. Column 1 contains a 3 in row 7, leaving r1c1 with {1, 2}. Column 2 contains a 1 in row 9, leaving r1c2 with {2, 3}. Column 3 contains a 1 in row 6, leaving r1c3 with {2, 3}. The top-left box contains 4–9, so it removes none of these remaining candidates.
- Look for the digit 1 across the row. It appears in only r1c1’s candidate list. Row 1 needs a 1 and the other two empty cells cannot hold it, so place 1 at r1c1.
- Update and scan again. Remove 1 from notes in cells sharing that row, column or box. The two other row-1 cells still allow 2 and 3 at this stage; this deduction alone does not tell you their order.
Before the placement, none of row 1’s three blanks is a naked single. The proof comes from counting locations for 1, not counting candidates in r1c1. You could also notice 1’s only location in the top-left box: either group gives the same certain placement.
Find hidden singles without filling every note
Pick a box and a digit absent from it. Trace the rows and columns containing that digit; their empty cells in the box are ruled out. Also ignore occupied cells. If exactly one empty cell survives, place the digit there. If two survive, neither is confirmed by this scan.
For a row, check the column and box of every empty cell for the digit you are tracking. For a column, check each empty cell’s row and box. Notes can help, but you can make the same deduction by elimination directly from the placed digits.
A practical scanning routine
- Start with a nearly complete group. List its missing digits, then check possible locations one digit at a time.
- Try a digit already placed in several nearby groups: those placements may rule out many locations in the group you are checking.
- After any placement, revisit the intersecting groups. It can expose both hidden and naked singles.
- If no single appears, change groups or try another deduction. Do not silently remove candidates just to make a single appear.
In Puzzuno, Notes records your own possibilities. Turn Notes off before entering the confirmed digit. The Sudoku How to Play guide explains touch controls, keyboard input, Undo and hints.
Common mistakes
- Counting only the notes you wrote. An omitted note in another cell can make a digit look unique. Check every empty cell’s legal possibilities before committing.
- Combining unrelated groups. The unique location must be within one particular row, column or box, not an arbitrary collection of cells.
- Treating tentative entries as proof. The deduction assumes the placed numbers are correct. If a missing digit has no legal location, review earlier entries and candidate calculations.
- Thinking two notes prevent a placement. Other candidates in the cell do not matter once one required digit has no alternative location in the group.
Frequently asked questions
Can a hidden single occur in a column?
Yes. Rows, columns and boxes each require 1–9 once. The same only-location argument applies to all three kinds of group.
Do I need to assume the puzzle has one solution?
No. With correct current placements, every valid completion must put the required digit in its only legal location. The deduction follows from the group rule, rather than an assumption about uniqueness.
Can the same move be both a naked and a hidden single?
Yes. A cell might have only one candidate while also being that digit’s only location in a group. The two names describe different ways to establish the placement; neither needs to exclude the other.
Will hidden singles solve every puzzle?
No. Some positions need other deductions. Finding no hidden single means this scan has not found a forced move, not that guessing is the only option.
Practice one complete deduction
Open Sudoku practice, choose a group and explain why a missing digit cannot occupy each alternative cell. Then try today’s Daily Challenges when you want a fresh shared puzzle. To compare the two beginner techniques, revisit the naked single example.