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.

... the question also doesn't state whether the ice must be H20 or, say, iced carbon dioxide.

Nor does it state that we can't be out in space, where there is no gravity.

Nor does it state that we couldn't have encased a lead pellet in the ice.

Nor does it state whether the iced water would taste better with a slice of lemon or a slice of lime.


... at a certain point it's useless to say "The puzzle is uncertain because it doesn't state X or Y". Obviously you have to assume there is no salt in the water, or that there are no other ice cubes pushing it down, or that the ice doesn't melt before you can measure how much is above the water. Those are pointless things to question.

What might have been a question was whether the size of the cubes mattered, but, as others have proved, the size of the cubes does not matter.



Things that do matter, such as tempurature, still do not need to be stated in the question. The puzzle states "...along with your assumptions." Therefore, if you start your answer saying "Assume the water around the ice is at zero degrees..." you can get an answer that's just as correct as if you say "assume the water around the ice is at 90 degrees...".

Edited on April 21, 2005, 5:45 pm

Posted by Sam on 2005-04-21 17:41:53