Monday, May 13, 2013

The Rule in Sudoku

There is only one rule in Sudoku: each row, each column, and each block must contain all digits 1 to 9. To understand this rule clearly, imagine the following partially filled Sudoku:
Column 5, Row 5, and Block 5 are filled with digits 1 to 9.
Verify that Column 5, Row 5, and Block 5 contains all digits 1 to 9. Good questions to ask yourself:
Are all digits 1 to 9 present in the column, row, or block?
Any digits appear more than once in the column, row, or block?

Let's look at how the rule can be violated. What happens if a row, a column, or a block happens to contain any same digit twice? Look at the next diagram:
An incorrectly filled Sudoku in Column 5, Row 5, and Block 5.
Again, ask these good questions: 
Are all digits 1 to 9 present in the column, row, or block?
Any digits appear more than once in the column, row, or block?

Correct observation reveals that:
a) Column 5, with Digit 3 appearing twice, is missing Digit 1.
b) Row 5, with Digit 1 appearing twice, is missing Digit 2.
c) Block 5, with Digit 2 appearing twice, is missing Digit 1.

Therefore in Sudoku, if you find yourself with any digit appearing twice in a row, a column, or a block, you will immediately realise that your Sudoku has been solved incorrectly. Retrace back to find the correct solution, or redo the whole Sudoku.

Good Sudoku 
A good Sudoku is designed to have only one unique set of Solution. It can be solved fully by logical reasoning, without the need to guess. Even the world's hardest Sudoku, AI Escargot, and Everest, can be solved by logical reasoning alone. Extremely high knowledge of Sudoku solving is required to solve these Sudoku. First things first, you need to learn the basic knowledge of Sudoku solving.

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