
Definitions
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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 (nm) degrees of freedom
 A set of n cells limited to m candidates
 Almost Hidden set with (nm) 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:
 One candidate in one large container
 One cell
 native weak set

 (given only a blank puzzle grid) One of the following weak sets:
 One candidate in one large container
 One cell
 continuous 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
 strong inference set
 a strong set
 strong link
 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
 weak link
 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. Also =.
 
 Binary weak link. (A  B) means ((notA) OR (notB)). Used in forbidding chains. Also 
 %
 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. Also []
 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.
Current Symbols
 =
 Binary strong link. (A = B) means (A OR B). Used in Alternating Inference Chains, Eureka style notation. Equivalent to == above.
 
 Binary weak link. (A  B) means ((notA) OR (notB)). Used in Alternating Inference Chains, Eureka style notation. Equivalent to  above.
 []
 Used in AIC to contain a Boolean variable that partitions more than
one native strong set. Equivalent to {} above.
Some Common abbreviations  sometimes in lower script  not an exhaustive list
 AIC
 Alternating Inference Chain, equivalent to a Forbidding Chain
 ALS
 Almost Locked Set
 AUR
 Almost Unique Rectangle
 BUG
 Bivalue Universal Grave  a puzzle state of only bivalues or bilocals, that would cause a puzzle to have more than one solution
 F..
 Finned (adjective)  usually refers to an Xwing, Swordfish, or some sort of Fish
 HP
 Hidden Pair
 HT
 Hidden Triplet
 HQ
 Hidden Quad
 LC
 Locked Candidate
 MUG
 a puzzle state that would cause a puzzle to have more than one solution, reserved usually for Multivalued cells and/or locals
 NP
 Naked Pair
 NT
 Naked Triplet
 NQ
 Naked Quad
 Q..
 Quantum (adjective), usually used to refer to a Locked Set of some kind that is atypical, or hybrid in some way
 SIS
 Strong Inference Set  a set that contains at least one true item
 SF
 SwordFish
 SSTS
 Simple Sudoku Technique Set/Solution/Stumped Point  not sure of the official designation for that last S
 STE
 Singles To End
 UL
 Unique Loop  a state, usually in bivalues or bilocals, that would causea puzzle to have more than one solution
 UP
 Unique Possibilities, equivalent to Naked Singles plus Hidden Singles
 WW
 W Wing  a type of YWS, two cells that contain the same bivalues both weakly linked to the same bilocal SIS
 XW
 X Wing
 YW
 Y Wing, or xYWing
 YWS
 Y Wing Style  a 3 SIS pattern similar in logic to the Y Wing
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

Naked Pairs, Triples, Quads,...
 Looks at strength of N candidates in N cells to deduce strength of those N
candidates in N locations within a large container(s)

Hidden Pairs, Triples, Quads,...
 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
 Advanced Forbidding Chains
 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
Please endure the definitions herein
 Puzzle coordinate system used here can be found at the
blog introduction
page.
Links to recommended sites

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