What is a Sudoku puzzle?

Sudoku or Su Doku is a Japanese word ("Suji wa dokushin ni kagiru") meaning something similar to "Number Place" or "Number Puzzle" or "Single Number" or "the numbers must be single" or "the numbers must occur only once"; The name Sudoku is a trademark of puzzle publisher Nikoli Co Ltd in Japan. Some people spell the name as "Su Doku". Sudoku became popular in Japan in 1986, Britain in late 2004, and internationally in 2005.Sudoku on Google Trendsexplains exactly when Sudoku became popular in the online world or the world wide web. Sudoku is often described as Rubik's cube of 21st century. The speciality of the Sudoku puzzle is that the completion rules are simple, yet the reasoning required to completion can be very difficult. A Sudoku puzzle contains a 9X9 grid, which comprises nine 3X3 sub-grids (also called as boxes or blocks). Some of the entries in the grid are filled with numbers from 1 to 9, whereas other entries are left blank. Click here for an example Sudoku puzzle. A Sudoku puzzle is solved by assigning numbers from 1 to 9 to the blank entries such that every row, every column, and every 3X3 sub-grid contains each of the nine possible numbers 1 to 9. Sudoku grids are special cases of Latin squares; Latin square of order n is an nXn square containing each of digits 1...n in every row and column. The numerals in Sudoku puzzle are used for convenience, and any kind of arithmetic relationship between the numerals is irrelevant. Any set of symbols, letters or shapes can be used instead of numerals. Many publishers like ESPN, Dell Magazines, Viz magazine, use leading actors in place, images of television series, positions in baseball fields instead of numerals.

Variants

9X9 grid comprising nine 3X3 sub-grids is the most popular variant of Sudoku puzzle. However Sudoku puzzles are also available in variety of other dimentions. It is very common to find 12X12 grid Dodeka Sudoku puzzles, comprising nine 4X4 sub-grids; 4X4 grids with 2X2 sub-grids; 5X5 grids with pentomino subgrids; 6X6 grids with 2X3 sub-grids; 7X7 grids with six heptomino sub-grids; 25X25 grids with twenty five 5X5 subgrids (Giant behemoths),and 21X21 (roughly) grid Samurai Sudoku puzzles with five overlapping 9X9 sub-grids. Multitude of additional variants can be obtained by enforcing more constraints. Once common constraint is requiring the numbers in the main diagonal to be unique.

Another interesting variation is the combination of Sudoku with Kakuro on a 9X9 grid, also called as "Cross Sums Sudoku". Kakuro Sudoku puzzles come with clues which are generally cross sums. The sums might be expressed using cryptic alphabets or numbers. A good example is NUMBER+NUMBER=KAKURO, which has a unique solution 186925+186925=373850. Another good example is SUDOKU=IS*FUNNY, whose solution is 426972=34*12558.

HyperSudoku is another variation of normal Sudoku; it looks like normal Sudoku, but has additional constraints. HyperSudoku contains 9X9 grids with 13 3X3 overlapping sub-grids. In addition to the nine 3X3 sub-grids in normal Sudoku, there are four more 3X3 sub-grids overlapping with normal nine 3X3 sub-grids in normal Sudoku. The additional four 3X3 grids are highlighted in blue color Fig 1.

As mentioned before, using alphabets or symbols instead of numerals with no functional difference are also found. We are also planning to introduce a variant that is a mix of crosswords and normal sudoku puzzles. Sudoku versions of Rubik's cubes known as Sudokube or Sudoku cube or Sudocube is also available. Fig 2 is an example Sudokube. Solving Sudokube is more difficult than solving Rubik's cube. There are many variations of Sudokube, some of them when solve have the number arranged in order, while others don't. The orientation of numbers is a vital information in Solving Sudokube. It is also important that one should understand how the cubes move around and interact with other cubes in order to solve both Sudokube and Rubik's cube. I will soon write a article on solving sudokube and link it here.