Glossary of Sudoku - Terms Related To Solving

Terms Related To Solving

The meanings of most of these terms can be extended to region shapes other than blocks. To simplify reading, definitions are given only in terms of blocks or boxes.

Scanning

The process of working through a puzzle to look for or eliminate values.

Cross hatching

Process of elimination that checks rows and columns intersecting a block for a given value to limit the possible locations in the block.

Counting

Process of stepping through the values for a row, column or block to see where they can or cannot be used.

Box line reduction strategy

A form of intersection removal in which candidates which must belong to a line can be ruled out as candidates in a block (or box) that intersects the line in question.

Candidate

Potential value for a cell.

Contingency

A condition limiting the location of a value.

Chain

A sequence of contingencies connected by alternative values.

Higher circuits

Related locations outside the immediate row, column and grid. The locations are related by value contingencies.

Independent clues

A set of clues that cannot be deduced from each other. Often depends on the order of choosing the clues for a given grid.

Intersection removal

When any one number occurs twice or three times in just one unit (or scope) then we can remove that number from the intersection of another unit. For example, if a certain number must occur on a certain line, then occurrences of that number found in a block that intersects this line can be ruled out as candidates. Sometimes called Pointing (or matched) Pairs (or twins)/Triples (triplets) as they point out a candidate that can be removed.

Trial and error

The process of guessing successive candidate values in conjunction with deductive elimination. A.k.a.: what-if, bifurcation, garden of forking paths, depth first search, exhaustive search, back-tracking search, Ariadne's thread. Note: there is no clear boundary between trial-and-error and the use of pattern recognition strategies to eliminate values (higher circuits), the latter being a condensed form of analysis based on elimination by contradiction, i.e. the same as what-if.

Nishio

What-if method of elimination, where the use of a candidate that would make its other (necessary) placements impossible is eliminated.

The One Rule

Fill in all (blank) cells so that each row, column and box contains the values 1-9. Same as: fill in the grid so that each row, column and box contains the values 1-9 exactly once, without changing the clues.

Single or singleton or lone number

The only candidate in a cell.

Hidden single

A candidate that appears with others, but only once in a given row, column or box.

Locked candidate

A candidate limited to a row or column within a block.

Naked pair

Two cells in a row, column or block, which together contain only the same two candidates. These candidates can be excluded from other cells in the same row, column or block.

Hidden pair

Two candidates that appear only in two cells in a row, column or block. Other candidates in those two cells can be eliminated.

Trio

Three cells in a unit sharing three numbers exclusively. See "Triples and quads".

Triples and quads

The concepts applied to pairs can also be applied to triples and quads.

X-wing

See N-fish (with N=2).

Swordfish

See N-fish (with N=3).

N-fish

Analogues of hidden pairs/triples/quads for multiple rows and columns. A pattern formed by all candidate cells for some digit in N rows (or columns), that spans only N columns (rows). All other candidates for that digit in those columns (rows) can then be excluded. Names for various N-fish:

• 2-fish: X-wing
• 3-fish: Swordfish
• 4-fish: Jellyfish
• 5-fish: Squirmbag – For 9×9 Sudoku, there's no in point naming higher-order (>4) fish, since every N-fish comes paired with a 9−N fish whose effect is the same (thus any 5-fish is paired with a jellyfish; any 6-fish with a swordfish; any 7-fish with an x-wing; any 8-fish with a hidden or naked single). Nevertheless, a 5-fish is occasionally called a squirmbag.
• 6+ fish: 6-gronk, 7-gronk ... – these patterns are only useful for Sudoku larger than 9×9.

Remote Pairs

When a long string of naked pairs that leads around the grid exists, any cells that are in the intersection of the cells at the beginning and the end of the string may not be either of the numbers in the naked pairs, for example, 4 and 7.