Expert

Forcing Chain

When every candidate of one cell forces the same conclusion.

Explanation

Pick a cell with few candidates and try each one in turn, following the resulting singles. If one assumption leads to a contradiction, that candidate can be removed. If every assumption forces the same digit into some other cell, that digit can be placed directly.

Forcing Chain example Sudoku board 4 2 9 1 5 7 5 3 1 9 8 5 5 7 6 2 8 7 6 8 4 3 4 9 5 1 3
An example board where Forcing Chain applies

Practice tip

Use this as a last resort. Start from bivalue cells: two short branches are enough for a conclusion.

Example steps

  1. Assume each candidate of the starting cell in turn.
  2. Follow the chain of singles that each assumption forces.
  3. Keep the shared conclusion: a contradiction removes a candidate, agreement places a digit.

Try this technique on a real puzzle.

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