Sudoku Puzzles

Frank Hilvers

Taylor O’Brien

The History of Sudoku

The history of Sudoku puzzles dates back to the 18th century. Swiss mathematician named Leonhard Euler

developed the concept of “Latin Squares” where numbers in a grid appear only once, across and up and down.

In the late 1970’s, Dell Magazines began publishing Sudoku puzzles using Euler’s idea with a 9 by 9 square grid. At that time it was called Number place and was created by a puzzle maker named Howard Garnes.

Number Place became known as Sudoku. “Su” means number in Japanese and “Doku” refers to

the single place on the puzzle board where each number fits into. Nikoli gave the puzzle this name.

Helped improve it by restricting the number of exposed or given numbers to 30 and having them appear symmetrically

It also means someone who is single can play; it has been described as “Solitaire with numbers”.

Benefits of solving a Sudoku Puzzle The Teacher’s Magazine recommended

Sudoku as a brain exercise in classrooms and suggestions have been made that Sudoku solving is competent of slowing the development of brain disorders, such as Alzheimer’s.

Mathematics

How many Sudoku solutions exist for each n? To put the question another way: Starting from a

blank grid—with no givens at all—how many ways can the pattern be completed while obeying the Sudoku constraints?

As a first approximation, we can simplify the problem by ignoring the blocks in the Sudoku grid, allowing any solution in which each column and each row has exactly one instance of each number.

On the smaller side, there's not much to say about the order-1 puzzle. The order-2 Sudoku (with 4 rows, columns and blocks, and 16 cells in all) is no challenge as a puzzle, but it does serve as a useful test case for studying concepts.

If you take any solution and rotate it by a multiple of 90 degrees, you get another valid grid.

The numerals in the cells are arbitrary markers, which can also be permuted; for example, if you switch all the 5s and 6s in a puzzle, you get another valid puzzle.

When all these symmetries are taken into account, the number of essentially different Sudoku patterns is reduced substantially.

Solving the puzzle

Solving a Sudoku puzzle can be easy or difficult (depending on what level of puzzle you choose to do). It’s best to start off with an easy puzzle and work your way up.

The easy ones have more “given” numbers and makes it easier to solve the grid, the more difficult ones have less and less numbers provided.

An unsolved puzzle

Solved Puzzle

Play Sudoku Online! WOWZERS!

http://www.websudoku.com

Make your own puzzle! http://www.puzzle.ro/en/sudoku_solver.htm