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ENVI

Naked Single

Sole Candidate

1-step reasoningDifficulty

A cell sees 8 different digits in its row, column and box, so only one possibility is left.

Rule

A cell's row + column + box contain 8 different digits → the cell is the 9th.

1122334455667788994913941916497283156469162871242

Pick a cell

Look at cell r4c5. It belongs to row 4, column 5 and box 5 at the same time — the three units it "sees".

The idea

This technique looks from the cell's side. Each cell "sees" 20 others: 8 in its row, 8 in its column and 4 more in its box. Collect the digits in those cells; if there are 8 different ones, the missing digit is the answer.

Once every cell has its candidates written in, naked singles stand out: they are cells with a single candidate. Without pencil marks you have to count, which is why this technique usually comes after the hidden singles run out.

How to spot it

  • Favour cells where a busy row crosses a busy column.
  • With pencil marks: look for a cell with just one small digit.

Common mistakes

  • Counting the same digit twice (say a 4 in both the row and the box) and thinking you already have 8.

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Related techniques

References

The examples on this page are generated from random puzzles, not taken from these sources.