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:
- 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 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
- 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.
- --
- 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
-
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
