Saturday, August 8, 2009

How To Play Sudoku

How To Play Sudoku

How to Play Sudoku?
Sudoku requires no calculation or arithmetic skills. It is essentially a game of placing numbers in squares, using very simple rules of logic and deduction. It can be played by children and adults and the rules are simple to learn.

Sudoku Objective
The objective of the game is to fill all the blank squares in a game with the correct numbers. There are three very simple constraints to follow. In a 9 by 9 square Sudoku game:
  • Every row of 9 numbers must include all digits 1 through 9 in any order
  • Every column of 9 numbers must include all digits 1 through 9 in any order
  • Every 3 by 3 subsection of the 9 by 9 square must include all digits 1 through 9
Similarly, smaller Sudoku puzzles, such as the 4x4 puzzle, must have the numerals 1 through 4 in each row, column and subsection. Larger Sudoku games (16 by 16) must have numerals 1 through 16 in each row, column and region. The principles are the same whatever the size of the game.

Every Sudoku games begins with a number of squares already filled in, and the difficulty of each game is largely a function of how many squares are filled in. The more squares that are known, the easier it is to figure out which numbers go in the open squares. As you fill in squares correctly, options for the remaining squares are narrowed and it becomes easier to fill them in. The Sudoku games on SudokuDaily.net let you check your progress as you go, to help prevent going down a wrong path.

Sudoku Solution Techniques

The first things to do in tackling a Sudoku puzzle is to scan the rows and columns to see where a certain number might go, given the 3 constraints listed above. For example, the fact that a 7 is required in the top right corner can be determined by first analyzing its 9 square sub-region. The only numbers missing in the region are a 5 and a 7. However, putting a 5 in the top right box would conflict with the 5 already in the top row and the rightmost column. The 7, on the other hand, would not conflict with any of the given numbers.

Once the 7 is filled in, deduction requires that only a 5 can go beneath it as all digits from 1 through 9 must be represented in the region. From there, one can turn to the two remaining open boxes in the right column - these must include a 2 and a 4 as the column's digits must represent 1 through 9. One of these options, placing the 4 beneath the 1, would lead to a conflict with the 4 already in that horizontal row, so the only option for this box must be a 2.

However, options for boxes are often not that easy to deduce. Another technique is to "pencil in" possibilities and then follow the possible solutions that emerge until a conflict is found. Often these conflicts appear after 2 or 3 numbers are penciled in, and one can return to the start and try the next option until something clicks.

The Sudoku puzzles on SudokuDaily.net make penciling in options very easy. Just put a possible number in a box, click on it, and it is moved to the top left light blue area of the box. From there you can start considering possibilities until the solution to a box or two emerges, or until you need to pencil in another option and start again.

The great thing about Sudoku is that every step makes the next step easier by narrowing possibilities. Every solved box makes filling the next box a little bit easier.