# Sudoku Definitions, Terminology and Glossary

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### General definitions

Almost Locked Set
A set in a common large container with 1 degree of freedom
Boolean variable
Any statement limited to two values. Usually, {TRUE, FALSE}.
candidate
A potential number in a cell
container
A defined partition of the Sudoku puzzle. A cell, box, row, or column.
degrees of freedom
Consider a set of cells in a common large container:
• Almost Naked set with (n-m) degrees of freedom
• A set of n cells limited to m candidates
• Almost Hidden set with (n-m) degrees of freedom
• A set of n candidates limited to m cells
depth
Number of native strong sets used to justify an elimination(s) (Sudoku only)
elimination
The exclusion of a candidate from a location
forbidding matrix
An n x n table that transparently illustrates an elimination(s)
house
container
large container
Box, Column, or Row.
native
adjective - Appearing within the current possibility matrix.
native strong set
Given the current possibility matrix, one of the following strong sets:
1. One candidate in one large container
2. One cell
native weak set
(given only a blank puzzle grid) One of the following weak sets:
1. One candidate in one large container
2. One cell
continuous nice loop
A wrap around forbidding chain
ntuple
A set with zero degrees of freedom. (Thus a hidden or naked pair, triple, etc.)
possibility matrix
The puzzle grid decorated with the remaining possible candidates for each cell
sees
Forbids by sharing a container with
strength in cell - also called naked strength
A reflection of the unwritten sudoku rule:
• A solved sudoku cannot contain a cell empty of all candidates
strength in location - also called hidden strength
A reflection of the written sudoku rule:
• A solved sudoku cannot contain a large house empty of any candidate
strong set
noun - A set of Boolean variables such that at least one is true
The logical operator OR (union). The endpoints of a strong link form a strong set
weak set
noun - A set of Boolean variables such that at most one is true
The endpoints of a weak link form a weak set
wrap around forbidding chain
A forbidding chain is called wrap around when the endpoints of the chain form a set that is both strong and weak.
Unique Possibility
A candidate that is a singleton in a container
UP
short for Unique Possibility or Unique Possibilities

### Symbols

==
Binary strong link. (A == B) means (A OR B). Used in forbidding chains.
--
Binary weak link. (A -- B) means ((notA) OR (notB)). Used in forbidding chains.
%
because it is a singleton in (container x). Used to describe a Unique Possibility.
<>
does not equal
=>
implies
~
not
ab1
shorthand for a1,b1
{}
Used in forbidding chains to contain a Boolean variable that partitions more than one native strong set
Subscripts
Used within forbidding chains to help clarify the partioning of a native strong set (strong inference set) that has more than one possible distinct partition. Possible examples:
• A cell with 3 or more possible canidates
• A candidate with 3 or more possible locations within a house.

### Technique definitions

Unique Possibilities
Finds singular strengths in any container
Locked Candidates
Looks at strength in location of one type of candidate in one large container to deduce strength of that candidate in location
Looks at strength of N candidates in N cells to deduce strength of those N candidates in N locations within a large container(s)
Looks at strength of N candidates in N locations within a large container(s) to deduce strength of those N candidates in N cells
Xwings, Swordfish, Jellyfish, Squirmbags
Looks at strength of one type of candidate in N rows(location) to deduce strength of that candidate in N columns(location) OR vice versa
Unique Rectangles
Looks at potential symmetrical overlapping strength of candidates in location to deduce strength of any type
Coloring
Looks at strength of one type of candidate in location to deduce strength of that candidate in location
Y wings
Looks at strength of 3 cells containing exactly 2 candidates each. Considers 3 types of candidates. Deduces strength of one of those candidates in location
Y wing style
Looks at 3 native strengths of any type to deduce strength(s) of any type
Forbidding Chains
Looks at any number of strengths of any type to deduce strength(s) of any type
A forbidding chain that uses a technique as a Boolean variable
Almost Locked Sets
In most locations, considers two sets with 1 degree of freedom each. Uses a weak link between them (relative location) to deduce strength. More generally, a forbidding chain that uses one or more ntuples as a Boolean variable.
Alternating Inference Chain
A Forbidding Chain

### Notes

• Native weak links are independent of the possibility matrix.
• Native strong links are dependent upon the possibility matrix.
• The operators, == and --, are not dependent on order. Thus, (A==B) is equivalent to (B==A)
• (A forbids B) is equivalent to (A -- B), and therefor also (B forbids A)
• (A -- B == C) => (A => C)
• Strong and weak are not mutually exclusive properties
• A set that is both strong and weak contains exactly one truth
• In most forbidding matrices, each row is a strong set
• Other sudoku sites may needlessly restrict the definition of
• strong
• weak
• coloring
• forbidding chains
• depth