Pencil marks that you can trust

Build complete candidate lists before relying on them.

A candidate is still possible

A candidate is a digit not yet ruled out for an empty cell. Start with 1 through 9. Cross out every digit already placed in the cell’s row, column, or box. The remaining digits are its legal candidates. Being legal does not promise that a candidate is the final answer.

For exampleIf those three groups contain 1, 2, 4, 6, 7 and 9, the cell’s starting candidate list is 3, 5, 8.

Notes are your scratch paper

You may write a few pencil marks while scanning. That is useful, but a partial note list cannot prove “these are the only possibilities.” Auto notes fills the complete legal list. The hint engine builds its own complete candidates, so a missing handwritten note cannot manufacture a false pattern.

For exampleWriting only 3 in a cell does not prove 3 if you simply have not checked whether 5 and 8 also fit.

Logical reductions go further

A technique can prove that a legal-looking candidate cannot lead to a valid completion. Erasing it is a logical reduction. Our guided hints keep verified reductions separately from your handwritten notes. Later hints use complete legal candidates minus those proved reductions.

For exampleThe row, column, and box may permit 8 locally, but a valid pair elsewhere can prove that this cell cannot use 8.

Recheck after editing

A placed digit immediately removes that digit from its peers. Erasing or changing an earlier entry can invalidate deductions that depended on it. Use Undo to go back through moves, or reset deductions to rebuild from the current entries. Never treat a pencil mark as an original clue.

For exampleIf you erase the 7 that excluded 7 from a neighboring cell, 7 may need to return to that cell’s legal list.

Quick check

You wrote only a small 4 in a cell, but have not checked its whole row, column, and box. Is that a naked single?

Yes, because there is one visible mark.
Not yet. First check that every other digit is ruled out.
No cell can ever be solved from pencil marks.

Show the answer

Not yet. First check that every other digit is ruled out. Exactly. A complete candidate list turns the observation into a justified placement.

Try it with the interactive lessons Play an easy puzzle

Next, when you are ready: Naked single.