Sudoku Hidden Singles: Find Where a Number Must Go

A Sudoku cell with several pencil marks can look unfinished even when its answer is already forced.

The trick is to stop looking only at the cell. Look at the row, column, or box around it instead.

Suppose a square could contain 3, 5, or 9. That does not seem decisive. But if it is the only place in its row where 5 can go, the answer must be 5. The other candidates disappear because the row still needs that number.

This is a hidden single, one of the most useful techniques to learn after the basic rules.

Two questions that reveal different singles

A naked single answers the question: “What number can go in this cell?”

Check the numbers already present in the cell’s row, column, and 3×3 box. If only one candidate remains, place it.

A hidden single answers a different question: “Where can this number go in this row, column, or box?”

The selected number has only one legal location within that area. Its destination may still have several candidates written inside it.

The word “hidden” describes how the answer is obscured by other pencil marks. It does not mean you need a complicated technique or an unseen clue.

A small example

Imagine a row with five empty cells. The row is missing 1, 3, 5, 7, and 9.

For this illustrative example, suppose you have checked every empty cell against its column and box, giving these complete candidate lists:

• Cell A: 1 or 3
• Cell B: 1, 3, or 7
• Cell C: 3, 5, or 9
• Cell D: 7 or 9
• Cell E: 1, 7, or 9

None of the cells is a naked single. Every cell has at least two possibilities.

Now scan for 5. It appears only in Cell C.

The row must contain a 5, and the other four empty cells cannot take it. Therefore, Cell C is 5, even though its list also contains 3 and 9.

Notice what this deduction does not tell you. It does not immediately settle the remaining four cells. One reliable placement is enough. Enter it, update the affected candidates, and continue from the new position.

Scan one number at a time

When a board feels crowded, comparing every pencil mark simultaneously can make a simple deduction hard to notice.

Choose one row and identify its missing numbers. Pick one of those numbers, then examine the empty cells one at a time.

For each cell, ask whether the same number already appears in its column or box. If so, that location is excluded. If exactly one location survives, you have a hidden single.

Repeat the process in columns and boxes. You do not need a hidden single in all three areas at once. A forced location in any one of them is sufficient.

If two locations remain, stop short of choosing between them. You have narrowed the search, but you have not proved an answer.

Keep the evidence stronger than the notes

A single pencil mark on the screen is not automatically a valid single.

Perhaps you forgot to write another candidate. Perhaps you erased a number without a reason. Or perhaps an earlier incorrect answer is affecting your notes.

Before committing to a hidden single, verify two things: the number is still missing from the chosen area, and every other empty cell really is excluded.

Incomplete notes can still help you think, but they cannot safely prove that a candidate occurs only once. You can either complete the candidate lists for that area or check the exclusions directly against the placed numbers.

The important part is the reason, not how tidy the notes look.

Recheck the area your move changed

After placing a number, revisit its row, column, and box. Related cells can no longer contain that value.

Sometimes this produces a naked single. Sometimes it leaves a different number with just one available position. Sometimes nothing obvious happens, and you need to scan elsewhere.

Do not expect every correct move to start a chain. The purpose of this routine is to catch consequences while they are easy to trace.

It also gives you a useful explanation for each entry: “This row needs 5, and these other cells cannot hold it.”

Practice without rushing the answer

OnlinePuzzle’s Sudoku includes pencil notes and hints that offer a direction before you apply a step. You can use the explanation to check your reasoning rather than immediately filling the suggested value.

For a focused practice session, look for one naked single and one hidden single. Explain the difference in your own words before entering them.

When you next get stuck, alternate between the two questions: what can fit in this cell, and where can this number fit in this area?

The board has not changed. Your view of the available information has.