> Oh, right. But if there are 2^50 possible items, 2^20 can be identified 
> without splitting things exactly in half, methinks.

Well yes almost, actually if you have 2^50 items the last thing you want to 
do is split in half at each stage.  You'll end up not being able to identify 
anything after 20 questions!

Assuming you want to maximise the number of identifiable items, you arrange 
your questions so that all of the 2^20 outcomes point to a unique object, 
apart from one which is the "unknown" branch.  Then you can uniquely 
identify 2^20-1 items, the rest being lumped in the "unknown" branch.

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