>> You just need to think of a question that will exactly split the 
>> remaining outcomes in half each time.
>
> I think as long as there's *something* down either branch, you're OK. I 
> don't think it has to split things in half.

I meant that to be able to recognise 2^20 things, you need to ask a question 
at each step that will split the set in half.  Otherwise you will end up not 
having enough questions left to uniquely identify each item.

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