Rooted: Created page with "In Sudoku, '''inference''' is the interaction between linked candidates, in particular when they are used in chains or loops. There is some discussion about t..."

2020-06-04T01:04:54Z

Created page with "In Sudoku, '''inference''' is the interaction between linked candidates, in particular when they are used in chains or loops. There is some discussion about t..."

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In Sudoku, '''inference''' is the interaction between [[link]]ed [[candidate]]s, in particular when they are used in [[chain]]s or [[loop]]s.

There is some discussion about the difference between inferences and [[implication]]s.

There are 2 types of inference. Strong and weak. There are also 2 types of links. [[Strong link]]s and [[weak link]]s. The type of link determines what type of inference you can use.
* Weak links allow you to use weak inference only.
* Strong links allow you to use strong inference or weak inference.
== Strong inference ==
Strong inference is caused by strong links, which can be found in [[bivalue]] cells or [[bilocal]] units. Strong inference can also stem from patterns with the term '''almost''' in their name. A well known example is the [[Almost Locked Set]].

For two candidates, named '''A''' and '''B''', the following strong inference deductions can be made:
* If '''A''' is false, '''B''' is true.
* If '''B''' is false, '''A''' is true.

Strong inference is represented in most notation systems by an equal sign: '''='''.
== Weak inference ==
Weak inference is caused by any type of link, strong or weak. Two candidates in a single cell or two candidate representing the same [[digit]] for two [[peer]]s all have weak inference that we can use.

For two candidates, named '''A''' and '''B''', the following weak inference deductions can be made:
* If '''A''' is true, '''B''' is false.
* If '''B''' is true, '''A''' is false.

Weak inference is represented in most notation systems by a dash sign: <code>-</code>.

== Alternating inference ==
To create chains or loops, the inference between subsequent pairs of candidates must alternate between strong and weak. Consider the following links:
* '''A''' weak link with '''B'''
* '''B''' strong link with '''C'''
* '''C''' strong link with '''D'''
* '''D''' strong link with '''E'''
* '''E''' weak link with '''F'''

You may be inclined to write the following chain:
<font color="red">A - B = C = D = E - F</font>
However, this chain uses the wrong inference between candidates '''C''' and '''D'''. This might be illustrated by showing the list of implications:
* If '''A''' is true, '''B''' is false.
* If '''B''' is false, '''C''' is true.
* If '''C''' is false, '''D''' is true.
* If '''D''' is false, '''E''' is true.
* If '''E''' is true, '''F''' is false.
There is no proper connection between the 3rd line and those preceding and succeeding it. Although '''C''' and '''D''' have a strong link, we must use weak inference to write a correct chain:
A - B = C - D = E - F
Alternating inference guarantees that the logic is sound from the first to the last node in the chain.

{{debate}}
[[Category:Chains and Loops]]

Inference - Revision history

Rooted: Created page with "In Sudoku, '''inference''' is the interaction between linked candidates, in particular when they are used in chains or loops. There is some discussion about t..."