Rooted: Created page with "A '''Forcing Net''' shows a contradiction or a verity which is caused by testing a candidate. Also known as '''Generalized Forcing Chain'''. The term '''Contradict..."

2020-06-04T01:21:13Z

Created page with "A '''Forcing Net''' shows a contradiction or a verity which is caused by testing a candidate. Also known as '''Generalized Forcing Chain'''. The term '''Contradict..."

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A '''Forcing Net''' shows a [[contradiction]] or a [[verity]] which is caused by testing a [[candidate]]. Also known as '''Generalized Forcing Chain'''. The term '''Contradiction Net''' is also used when the Forcing Net is used to derive a contradiction.

There are several techniques similar to Forcing Nets, like [[Trial & Error]], [[Tabling]] and [[Bowman Bingo]]. Unlike a [[Forcing Chain]], which requires a single stream of [[implication]]s, a Forcing Net allows branching and merging, making it a lot more complicated than a single [[chain]]. Whenever possible, players avoid this [[solving technique]].

== How it works ==
The player selects a candidate to be tested. When this candidate belongs to a [[bivalue]] [[cell]], finding a contradiction allows the player to place the remaining candidate in that cell. The tested candidate is assumed to be true and the implications are analyzed until a contradiction is found or no further progress can be made.

Here is an example:

[[Image:Forcing net.png]]

This is the Forcing Net shown in the picture:
| r1c1<>9 => r1c2=9 => '''r6c2<>9'''
r1c1=2 =>| r3c2<>2 => r3c2=4 => '''r6c2<>4'''
| r1c6=7 => r1c9<>7 => r3c9=7 => r3c9<>2 =>|
| r1c9<>2 => | r6c9=2 =>| r6c8=3 => '''r6c2<>3'''
| '''r6c2<>2'''
The initial placement causes 4 branches, 2 of them merging further down the net and branching off again. Together, they eliminate all 4 candidates in '''r6c2''', which leaves this cell without any candidates.

As a result, we can eliminate candidate '''2''' from '''r1c1'''.

== Note ==
There is a disagreement over using Contradiction Nets to solve Sudokus puzzles. While some players make extensive use of Contradiction Nets since it is entirely logical from an angle, other players have accused that using Contradiction Nets is not anything different from using [[Ariadne's Thread]].

== External link ==
* [http://homepages.cwi.nl/~aeb/games/sudoku/solving22.html Generalized forcing chain]

[[Category:Solving Techniques]]
[[Category:Chains and Loops]]

Forcing Net - Revision history

Rooted: Created page with "A '''Forcing Net''' shows a contradiction or a verity which is caused by testing a candidate. Also known as '''Generalized Forcing Chain'''. The term '''Contradict..."