A Possibly easy for you, but hard for me Question about Sudoku

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The discussion centers on calculating the maximum number of valid patterns on a 9x9 Sudoku board, with a request for generalized answers applicable to NxN boards. The user is developing a Sudoku solver and expresses curiosity about the mathematical aspects of Sudoku configurations. References to Wolfram MathWorld are mentioned as valuable resources for further exploration of the topic. Participants are encouraged to provide insights and methodologies for determining valid Sudoku patterns. The conversation highlights the complexity of Sudoku and the interest in its mathematical foundations.
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A "Possibly easy for you, but hard for me" Question about Sudoku

How to calculate the maximum number of valid patterns on a 9x9 Sudoku board?

I was coding a flash application which is basically a "sudoku solver". This question is not related with qhat I'm doing but just curious.

Please, generalize your answers to NxN boards also, if you can.
 
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Wolfram MathWorld has a pretty interesting entry about Sudoku. There are also a couple of noteworthy references to read as well.
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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