MattM wrote:

> Is your question even related? Who said anything about finite?

http://en.wikipedia.org/wiki/Recursive_set

"A subset S of the natural numbers is called recursive if there exists..."

"Every finite or cofinite subset of the natural numbers is computable."

Thus, the answer to my question is no. In order words, there exist no 
finite sets which are not recursively enumerable.

Thus, as we have agreed the set of possible things to classify is not 
recursively enumerable, we can conclude that it is not finite.

It is impossible to decide on an element of an infinite set using a 
finite number of questions.

Thus, we can conclude that the game is in fact impossible to solve in 
general.

Goodbye.

-- 
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