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 (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 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 Multi-valued 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

• Sudopedia
• Forbidding Chains for Absolute Beginners
• Sudoku Players' Forums
• Sudoku Discussions