Digit Forcing Chains

Expert

Run inference chains from each possible position of a digit; if all chains reach the same conclusion, it must be true.

How It Works

For a digit confined to a few cells in a unit, run inference chains from each possible position. If every chain leads to the same conclusion (a placement or elimination), that conclusion is certain regardless of where the digit actually goes.

Based on the "all paths lead to the same result" principle.

Example

3456
256
8
35
14
9
1257
24
67
1
259
3459
35
67
259
248
89
456
7
4569
2
14
8
159
3
69
25
59
1873
29
64
347
8
34
692
37
15
2367
69
369
154
2379
28
789
56
3
56
781492
842935671
917426853
Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Practice with a Real Puzzle

This 9×9 puzzle is solver-verified to require this technique on its solution path.

Expert25 givens