Some questions appear clear, but are deceptively difficult to define, and their answer is very sensitive to the exact technical definition of the question, in such a way that it renders the original question almost meaningless.
What would you call such a question?
How many islands are there in Denmark?
According to wikipedia (http://en.wikipedia.org/wiki/Denmark#Geography_of_Denmark), there are 72 inhabited islands, 443 named islands, and 1419 islands above 100 square meters. However, it does not list how many islands there are in total, since it is so hard to define what constitutes an island. Some islands would be extremely small, and others tidal. Islands are created and destroyed by geothermal activity so you would have to specify a time or take it as the time of asking. Also, sometimes a peninsula (e.g. Jutland) may be considered an island if it is separated from the mainland by rivers.
How many words are there in English?
It depends on which dictionary you look at
What proportion of the laws of the United Kingdom are made in the European Union?
This was a subject of an article on the BBC's Radio 4 programme 'More or less'. It is difficult to define what is a law, since there are statutory instruments and various regulations that may or may not be counted. Also, some laws implement European Union law, others just refer to it. I believe the program said the total could be between 7-50%, depending on your definition.