You have a cube of ice floating in a glass of water. The question is what fraction of the ice will be above the water line? Assume that the ice is not bobbing.

Most of you have probably heard the answer to this before. But please provide a proof or solution, along with your assumptions.

You are right to mention that nothing is mentioned whether it is salt water or sea water or river water and that is why the answer is uncertainty.  You just assume that it must be pure water.  How could that be if the question does not mention the assumption and it is up to us for imagination.  Could it be sea water that is subject to the change of density?

What you say is correct.  The word, float, is mentioned in the question.  However, small ice cube like 1 cubic centimeter still floats.  However, it disappears a minute later and still the answer is uncertainty.  When it disappears, nothing is left.

You have given a lot of assumptions to this question in which the question is not mentioned and you expect the people to follow the rigid rules to solve the question, that is not practicable.  A good puzzle demands our creativity to solve the problem and not to give any assumption to any question if the question is not stated.