Forcing Chains and Nets

Assume a candidate is true and follow every consequence (singles, eliminations). Do the same for the other possible candidates in a cell, or for the other positions of a digit in a unit. If all branches end in the same conclusion (a placement or an elimination), that conclusion is a fact.

Forcing chains follow one chain at a time. Forcing nets may use any number of consequences, including singles, at each step, and are the hardest logical techniques HoDoKu searches for.

Notation

Forcing Chain Contradiction: 4 can be removed from r1c7. chain: 4 in r1c7 → 6 in r1c7 → 6 in r7c7 → 3 in r7c7 → 3 in r7c5 → 1 in r7c5 → 1 in r7c7 → 1 in r8c7 → 4 in r8c7 → 4 in r1c7. Assuming the first candidate is true leads, step by step, to the same cell not being that candidate: a contradiction, so it can be removed.