Forcing Fallback

Exhaustive forcing: every alternative of a source cell or house is tested and only conclusions shared by all branches are kept.

Forcing Chain

An open mixed X/Y implication chain that proves a placement or elimination.

Nishio

A single-value assumption is disproved by a contradiction.

Cell Forcing Net

Every candidate in one source cell leads to the same conclusion.

Region Forcing Net

Every possible position for a digit in one house leads to the same conclusion.

Dynamic Forcing Chain

Candidate consequences discovered during the chain create new implications.

Dynamic Forcing Chain Plus

A dynamic chain that can use an additional level of sub-rules.

Nested Forcing Chain

Forcing-chain deductions are nested inside another forcing chain.

When branching is the honest tool

These methods deliberately use case analysis. A forcing net starts from an exact-one constraint — every candidate of a cell, or every position of a digit in a house — and keeps only the conclusions shared by all branches. Nishio tests a single candidate and retracts it when the branch contradicts the rules for that digit.

Dynamic Forcing Chains let implications discovered mid-branch extend the analysis, and the nested form allows a chain to invoke another inside it. They are the most powerful entries in this reference and also the closest to trial and error: each page states the source set and the shared conclusion explicitly so the deduction can still be checked.

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