Sudoku X · Medium

Locked Candidates in Sudoku X

When a house can place a digit only where it meets another house, the digit is eliminated from the rest of that other house.

The idea

If every cell in a house that can take a digit also lies in a second house, the digit must go in that shared part. The rest of the second house cannot have it.

A diagonal crosses three boxes and every row and column, so it locks against all of them: a diagonal can lock a digit into a box or a line, and a box or line can lock one onto the diagonal.

Worked examples

3 positions from real Sudoku X puzzles on this site, the familiar case first. Step through each one: the board lights what each step talks about, and the arrows show what rules what out.

A box and a line, as in Classic

Medium puzzle · Locked Candidates

In box 4, find every cell that can still take 8.

Step 1 of 4Step 2 of 4Step 3 of 4Step 4 of 4

A diagonal locks a digit into a box or line

Medium puzzle · Locked Candidates

Start on the lit diagonal. It is a house, so its candidates for one digit can lock.

Step 1 of 5Step 2 of 5Step 3 of 5Step 4 of 5Step 5 of 5

A digit locked onto a diagonal

Medium puzzle · Locked Candidates

This time candidates are eliminated along the diagonal. It counts like a row.

Step 1 of 5Step 2 of 5Step 3 of 5Step 4 of 5Step 5 of 5

Where it fits

MediumLocked Candidates is a Medium technique: Medium Sudoku X puzzles are the first to need it.

The Classic Locked Candidates lesson teaches it on a plain 9×9 board. The Sudoku X overview explains the rule and the levels.

Locked Candidates in the other styles: Jigsaw, Thermo, Windoku, Arrow, Kropki.

Try it on a Medium Sudoku X puzzle. Next Step points it out when it is the move.

The worked examples, every step

A box and a line, as in Classic

Medium Sudoku X puzzle · Locked Candidates

  1. In box 4, find every cell that can still take 8.
  2. All of them (R5C3, R6C3) are also in column 3. Box 4 must have an 8 somewhere in those cells, so the rest of column 3 cannot. The arrows point to the cells that lose 8.
  3. Eliminate 8 from R7C3, R8C3, R9C3.
  4. Done: 8 is eliminated from R7C3, R8C3, R9C3.

A diagonal locks a digit into a box or line

Medium Sudoku X puzzle · Locked Candidates

  1. Start on the lit diagonal. It is a house, so its candidates for one digit can lock.
  2. On the main diagonal (from R1C1 to R9C9), find every cell that can still take 6.
  3. All of them (R4C4, R6C6) are also in box 5. The main diagonal must have a 6 somewhere in those cells, so the rest of box 5 cannot. The diagonal counts as a house here, like a row. The arrows point to the cells that lose 6.
  4. Eliminate 6 from R4C6, R6C4.
  5. Done: 6 is eliminated from R4C6, R6C4.

A digit locked onto a diagonal

Medium Sudoku X puzzle · Locked Candidates

  1. This time candidates are eliminated along the diagonal. It counts like a row.
  2. In box 5, find every cell that can still take 8.
  3. All of them (R4C4, R6C6) are also on the main diagonal (from R1C1 to R9C9). Box 5 must have an 8 somewhere in those cells, so the rest of the main diagonal cannot. The diagonal counts as a house here, like a row. The arrows point to the cells that lose 8.
  4. Eliminate 8 from R7C7.
  5. Done: 8 is eliminated from R7C7.

Previous: Hidden Single · Next: Naked Pair