MHB 8 Queens Problem (For people who want a try, not homework$)

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Imagine an 8x8 chess board. In how many ways can 8 queens be placed on the board such that no queen can "eat" any other queen.
 
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You might find http://mathhelpboards.com/potw-university-students-34/problem-week-167-june-9-2015-a-15548.html?highlight=queen relevant.
 
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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