Build accurate candidate notes

A candidate is a number that could legally occupy an empty square. To find candidates, remove every number already present in that square’s row, column, and box from the set 1 through 9.

Candidate notes are useful only when they stay current. After every answer, remove that number from the notes in its row, column, and box. The game handles this cleanup for answers you enter, which makes patterns easier to see.

Naked singles

A naked single is a square with only one candidate. If a square can contain only 7, then 7 must go there even when its row or box has several other empty squares.

Scan all candidate notes after each placement. A note removed in one part of the board can leave a newly naked single somewhere else.

Hidden singles

A hidden single appears when a number has only one possible square within a row, column, or box, even though that square still shows several candidates. The answer is hidden among the other notes.

Choose one missing number and look across a whole group. If every square except one is blocked by its crossing row, column, or box, place the number in the remaining square.

Locked candidates

Suppose every candidate 4 in one 3 × 3 box lies on the same row. The 4 for that box must occupy one of those squares, so no other square in that row outside the box can be 4. This is often called a pointing pair or pointing triple.

The idea also works in reverse. If all candidates for a number in one row fall inside the same box, remove that number from the other squares in the box.

Naked pairs

If two squares in one row, column, or box contain the same two candidates and no others, those two numbers must occupy those two squares in some order. Remove both candidates from every other square in that group.

The pair may not tell you which number goes in which square yet. Its value is the elimination it creates elsewhere, often producing a single.

How to work through a hard puzzle

Hard Sudoku is less about discovering one spectacular move and more about repeating a dependable loop. Clean notes, a consistent scan order, and returning to simple techniques after every change keep the puzzle manageable.

  • Find every naked single before looking for a more complex pattern.
  • Check each missing number for hidden singles in rows, columns, and boxes.
  • Compare candidate positions inside each box to spot locked candidates.
  • Look for identical two-number notes that form naked pairs.
  • After any elimination, return to singles before searching for another pair.