Sudoku is a puzzle in which the blank cells must be filled such that
each row, column and 3x3 box contains the numbers 1 to 9. The Sudoku7
program helps solving Sudoku puzzles.
Sudoku solving strategies
When solving a Sudoku it is helpful to maintain a list of possible values
or candidates for each blank cell. Maintaining the candidates by hand is
a boring and errorprone task. Luckily the Sudoku7 program helps by
automatically maintaining candidates. In Sudoku7 it is also possible to
mark cells according to a specific candidate or according to the number
of candidates.
There are several strategies which help to determine the value of cells
or allow to reduce the number of candidates. This solving strategies
have the following names: singles, hidden singles, locked candidates,
naked pairs, naked triples, naked quads, hidden pairs, hidden triples,
hidden quads, xwing and swordfish. The logic of the solving strategies
is described below. Sudoku7 can also apply the solving strategies
automatically.
Singles
When a cell has only one candidate the value can safely be assigned.
Hidden singles
Frequently a candidate is restricted to one cell in a row, column or
3x3 box (no other cell in that row, column or 3x3 box contains this
candidate). The cell containing this candidate may also have other
candidates. Since the cells in every row, column or 3x3 box must contain
the numbers between 1 to 9 this value can safely be assigned.
Locked candidates
Sometimes a candidate within a 3x3 box is restricted to one row or column.
In this case one of the restricted cells must contain the specific
candidate. Therefore the candidate can safely be excluded from all cells
in that row or column outside the 3x3 box.
Sometimes a candidate within a row or column is restricted to one 3x3 box.
In this case one of the restricted cells must contain the specific
candidate. Therefore the candidate can safely be excluded from all cells
in that 3x3 box outside the row or column.
Naked pairs
A naked pair consists of two cells in a row, column or 3x3 box which
contain an identical pair of candidates and no other candidates. In this
case the two candidate values must be in the two cells. Therefore the
two candidates can be excluded from the other cells in that row, column
or 3x3 box.
Naked triples
A naked triple consists of three cells in a row, column or 3x3 box which
contain no candidates other than the same three candidates. It is not
necessary that all three cells contain all three candidates of the triple.
In the case of a naked triple the three candidate values must be in the
three cells. Therefore the three candidates can be excluded from the other
cells in that row, column or 3x3 box.
Naked quads
A naked quad consists of four cells in a row, column or 3x3 box which
contain no candidates other than the same four candidates. It is not
necessary that all four cells contain all four candidates of the quad.
In the case of a naked quad the four candidate values must be in the four
cells. Therefore the four candidates can be excluded from the other cells
in that row, column or 3x3 box.
Hidden pairs
A hidden pair is defined by two candidates which are restricted to two cells
in a row, column or 3x3 box (no other cell in that row, column or 3x3 box
contains one of the two candidates). In this case the two candidate values
must be in the two cells. Therefore the other candidates in the two cells
can be excluded.
Hidden triples
A hidden triple is defined by three candidates which are restricted to three
cells in a row, column or 3x3 box (no other cell in that row, column or
3x3 box contains one of the three candidates). In this case the three
candidate values must be in the three cells. Therefore the other candidates
in the three cells can be excluded.
Hidden quads
A hidden quad is defined by four candidates which are restricted to four
cells in a row, column or 3x3 box (no other cell in that row, column or
3x3 box contains one of the four candidates). In this case the four
candidate values must be in the four cells. Therefore the other candidates
in the four cells can be excluded.
XWing
Sometimes there are two rows and two columns and the same candidate is
present at the four crossings between the rows and columns. When the
rest of the two rows or the rest of the two columns does not contain
the specific candidate the constellation is called xwing. In an
xwing the candidates must be in the diagonally opposite corners of
the rectangle formed by the four crossings. Therefore the specific
candidate can be excluded from all cells in the two rows and in the two
columns, except for the four corners of the xwing.
Swordfish
Sometimes there are three rows and three columns and the same candidate
is present at some of the nine crossings between the rows and columns.
When the rest of the three rows or the rest of the three columns does
not contain the specific candidate the constellation is called swordfish.
In a swordfish the candidates must be at three of the nine crossings
such that they do not share a row or column. Therefore the specific
candidate can be excluded from all cells in the three rows and in the
three columns, except for the nine crossings of the swordfish.
