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Is it known which quandles arise as the knot quandle of some knot? I seem - vaguely - to remember hearing that all (finite?) quandles arise this way but I've failed to find a reference to this fact.

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Personal anecdote, John Stallings showed me the initial knot quandle paper, showing that the quandle did a wonderful job of classifying knots. His comment was that there were plentiful imponderables, such as deciding whether a prescribed quandle was trivial. – Will Jagy Nov 3 '10 at 17:25
    
what is a quandle? – Paolo Aceto Nov 3 '10 at 18:14
    
en.wikipedia.org/wiki/Racks_and_quandles $$ $$ – Will Jagy Nov 3 '10 at 19:16
    
@Will-Jagy, so a quandle has to have both the right-distributive and the left-distributive properties of a rack, along with having $a\triangleright a=a$ and $a \triangleleft a = a$? Is the matrix-form the best way to represent it? (sorry to be asking another question as a comment...) – sleepless in beantown Nov 7 '10 at 3:48
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Each knot quandle is connected. – Zhiyun Cheng Apr 23 '14 at 9:33

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