## Recreational Math## Math Puzzles |

## What is the popular game of Sudoku? |

Sudoku (pronounced soo-doo-koo, not the incorrect sa-doo-ko) is a very popular mathematically based puzzle game that has somewhat mysterious origins. According to puzzle expert Will Shortz, the modern version of Sudoku was probably developed by Howard Garns (1905–1989), a retired architect and freelance puzzle constructor. In 1979, Garns published something called “Number Place” in a Dell magazine, a popular publisher of number, letter, and word games. But it took just over two decades for the game to be noticed in any detail. At that time, it was brought out by the Japanese puzzle company Nikoli under the name Sudoku, which means “single number” in Japanese. But in reality, it actually took until around 2005 to truly make Sudoku a household name (Garns died in 1989, so he never saw his invention become popular).

Sudoku doesn’t require any calculations or arithmetic skills, but is actually a game of placing numbers in squares using simple rules of logic and deduction. (Because of this, it is a game loved by young and old alike.) The overall game is played on a large grid that contains nine 3-by-3 grids that are partially “solved” by the person developing the puzzle. The objective is to fill in the remaining numbers in the entire 9-by-9 grid so that each column, row, and each of the nine 3-by-3 (called boxes, blocks, regions, or sub-squares) contain all the digits from 1 to 9. There is usually only one solution; when completed, the result is essentially a type of Latin square (see above) with the squares being individual sections that make up the entire 9-by-9 grid.

There are definite rules, too. For example, the same single number cannot appear twice in the same 9-by-9 playing-grid row or column; and the same number cannot appear twice in any of the nine 3-by-3 blocks of the entire playing grid. As long as the puzzle comes with at least 17 digits already placed on the grid, it is considered a solvable, one solution Sudoku. If there are less than 17 digits, then the puzzle has more than one possible solution, and therefore the game cannot be solved properly.

It may seem mathematically simple, but the 9-by-9 grid means there are 81 numbers that have to fall into the correct sequence, which means there are millions of possible combinations. Mathematically, the total number of possible digit combinations on a standard Sudoku grid is 6,670,903,752,021,072,936,960. But most mathematicians argue that many of these combinations are identical, only seen on the grid backward or rotated. Figuring out the number again shows there are 3,359,232 possible combinations. Thus, in a way, that is the total number of possible Sudoku puzzles. If you’ve only solved a half dozen, you have a long way to go!