Unique Solution

mcarne5252 · Posted: Thu Apr 20, 2006 1:51 am Post subject: Unique Solution

Can someone provide an explination or proof, perhaps using the idea of Latin Squares, on why a proper sudoku puzzle will always have one unique solution?

Thanks

Ruud · Site Admin

I'm not sure what you're asking for.

A sudoku is a proper sudoku because it has a unique solution. It is a qualification by convention.

You can examine a sudoku with a backtracking solver. When the solver finds exactly one solution, you may label it 'proper'.

If this is not what you're looking for, please explain what you need to know,

Ruud.
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coloin · Posted: Thu Apr 20, 2006 8:38 am Post subject:

There are three aspects here:
the final grid
the given clues
the generated clues

the final grid has to be valid before you start

Papy · Posted: Thu Aug 17, 2006 11:13 am Post subject: Unique solutionn

You don't have to proof that there is only one solution:
by definition a sudoku grid have only one solution!!!
Multiply solutions don't dive sudoku
Papy

Catweazle · Posted: Fri Aug 18, 2006 2:42 am Post subject:

I agree with Papy.

If a sudoku has more than one solution, you simply cannot solve the puzzle with logic.
And therefore it is no puzzle because you cannot finish it.
This because at a certain point you do not have a clue which number to fill in next.
Therefore a sudoku puzzle has to have 1 solution so it can be solved with logic until the end.

I hope this answers your question fully.

Theo
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