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Contradiction

The state of the grid in which the puzzle no longer complies with the rule.

Aliases include conflict and error.

A contradiction is an essential part of Trial & Error and related solving techniques. It is also used in the proof for other advanced solving techniques, but not necessarily used when such a technique is employed by a player.

When a contradiction is found, either the puzzle or a previous move is invalid. Since most solving techniques depend on a valid puzzle, the move is assumed to be invalid. This allows the player to perform the complementary move.

Contradiction Types

No candidates left in a constraint.

All candidates have been eliminated.

2 or more different candidates forced into a single constraint.

This is a conflict, because only one of these candidates can belong to the solution.

Depending on the way the solving technique is implemented, the second type can easily be transformed into the first type by letting one of the conflicting candidates eliminate the other.

This page was last modified 18:21, 11 October 2007.  

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