The modern puzzle was invented by an American architect, Howard
Garns, in 1979 and published by Dell Magazines under the name
"Number Place". It became popular in Japan in 1986, after
it was published by Nikoli and given the name Sudoku, meaning
single number. It became an international hit in 2005.
The strategy for solving a puzzle may be regarded as comprising
a combination of three processes: scanning, marking up, and
analyzing. The approach to analysis may vary according to
the concepts and the representations on which it is based.
top right region must contain a 5.
By hatching across and up from 5s elsewhere,
the solver can eliminate all
the empty cells in the region which
cannot contain a 5. This leaves only
one possibility (shaded green).
Scanning is performed at the outset and throughout the
solution. Scans need be performed only once between
analyses. Scanning consists of two techniques:
Cross-hatching: The scanning of rows to identify
which line in a region may contain a certain numeral
by a process of elimination. The process is repeated
with the columns. It is important to perform this process
systematically, checking all of the digits 1–9.
Counting 1–9 in regions, rows, and columns to
identify missing numerals. Counting based upon the last
numeral discovered may speed up the search. It also
can be the case, particularly in tougher puzzles, that
the best way to ascertain the value of a cell is to
count in reverse—that is, by scanning the cell's region,
row, and column for values it cannot be, in order to
see what remains.
Advanced solvers look for "contingencies" while scanning,
narrowing a numeral's location within a row, column, or region
to two or three cells. When those cells lie within the same
row and region, they can be used for elimination during cross-hatching
and counting. Puzzles solved by scanning alone without requiring
the detection of contingencies are classified as "easy"; more
difficult puzzles are not readily solved by basic scanning
Logically, every sudoku puzzle, regardless of difficulty,
is solved via scanning heuristics. In a true sudoku puzzle,
every number has a necessary position in each part of the
grid which can be deduced from the description or if you prefer
definition of what a "true" sudoku is. The only difference
between solving advanced puzzles and simpler puzzles is not
the techniques used to solve the puzzle but recognizing the
logical implications of the scanning heuristic. One such implication
would be recognizing logical "contingencies" which just basically
means narrowing down the possibilities of a given square via
the relations between every other square.