The small numbers tell the bigger story.

A candidate is a possibility, not a guess

In a standard 9 × 9 Sudoku, every row, column and 3 × 3 box must contain digits 1 through 9 once each. For an empty cell, candidates are the digits still compatible with those constraints and with earlier valid eliminations.

A small 7 in a cell does not mean “I think this is 7”. It means “7 has not been ruled out here yet”. Our coach shows automatic candidates and keeps earlier deductions when a step removes a possibility.

Two ways a number can become certain

A naked single is a cell with only one candidate left. The evidence comes from the values in its row, column and box, plus any previously justified exclusions.

A hidden single works the other way around: a digit has only one remaining place in an entire row, column or box, even if that cell still has other candidates. The coach highlights the relevant unit and identifies the unique location.

A useful step may remove a candidate

Suppose every remaining position for a digit in a box lies in one row. That digit must occupy that row within the box, so it cannot also appear elsewhere along the same row. The reverse relationship, from a line into a box, is useful too. These are locked-candidate deductions.

A naked pair is two cells in the same unit that each allow exactly the same two digits. Those two cells reserve those digits between them. A hidden pair is two digits that share exactly the same two possible locations; other candidates in those locations can be removed.

The reason is the constraint, not a completed answer grid hidden behind the interface.

What X-Wing adds

For one digit, look for two rows that each have exactly two candidate positions in the same two columns. Whichever diagonal is used, those columns will receive the digit in the two selected rows. Other candidate occurrences in those columns can therefore be removed. The same idea works with rows and columns swapped.

The four corner cells are the evidence. The cells where candidates are removed are the targets. The coach uses different highlights for these two roles.

A unique solution does not make every number an explanation

An independent search can establish whether a puzzle has a unique completion. That does not explain why a particular next move is justified by a human-style rule. Our logical coach does not look up the final answer to invent a reason.

If the supported techniques run out, the lesson stops and says so. Optional search lessons explicitly label assumptions and backtracking. A deduction inside an assumption branch is conditional on that branch; it is not presented as a proven fact about the original puzzle.

Keep clues separate from your own progress

In the Sudoku coach, use Original clues for the printed puzzle and My progress for numbers you entered yourself. Original clues stay locked in progress mode. A conflicting or unsatisfiable position may come from a copied clue or a mistaken move; the site does not pretend it can always identify the single wrong cell.

Back restores both values and candidate notes. Entering your own next move clears the old replay path and lets you analyze the actual board again.

For detailed technique definitions and examples, see HoDoKu’s singles reference and technique index.