Re: Sudoku Construction ?

On Sat, 17 Sep 2005 16:31:27 GMT, "Androcles" <Androcles@ MyPlace.org>
wrote:
you didn't read my question --- "in order to assure a unique
solution"
>
>"mathedman" <mathedman@xxxxxxxxxxxxxxx> wrote in message
>news:432c311f.87529944@xxxxxxxxxxxxxxxxxxxxxxxxxxx
>|
>| I read somewhere recently that a puzzle enthusiast has written
>| a computer program to produce Sudoku puzzles.
>| What type of algorithm/method is used to construct these
>| puzzles in order to assure a unique solution?
>
>Exhaustion. Computers are fast, so time doesn't matter.
>
>For a magic square, integers 1 to 9, sum 15 in rows and columms:
>
>Step 1:
>Place an integer random number 'a' within the required range at a random
>location.
>
>+---+---+---+
>| x | x | x |
>+---+---+---+
>| a | x | x |
>+---+---+---+
>| x | x | x |
>+---+---+---+
>
>Step 2:
>Place a second random number b not equal a at some other location.
>
>+---+---+---+
>| x | x | x |
>+---+---+---+
>| a | x | x |
>+---+---+---+
>| b | x | x |
>+---+---+---+
>
>Step 3:
>Here c is determined.
>
>+---+---+---+
>| c | x | x |
>+---+---+---+
>| a | x | x |
>+---+---+---+
>| b | x | x |
>+---+---+---+
>
>If c<=0, back up and change b. Goto Step 2.
>
>Step 4:
>Place another random number d not equal a,b,c somewhere.
>+---+---+---+
>| c | x | x |
>+---+---+---+
>| a | x | d |
>+---+---+---+
>| b | x | x |
>+---+---+---+
>Step 5:
>Here e is determined.
>+---+---+---+
>| c | x | x |
>+---+---+---+
>| a | e | d |
>+---+---+---+
>| b | x | x |
>+---+---+---+
>
>If e = a, b,c,d, or e<=0, goto Step 4.
>And so on.
>
>Eventually the computer will place 5 at the centre and solve the square.
>+---+---+---+
>| 6 | 7 | 2 |
>+---+---+---+
>| 1 | 5 | 9 |
>+---+---+---+
>| 8 | 3 | 4 |
>+---+---+---+
>Other methods are of course possible.
>
>Androcles
>
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