><i>You might be thinking, wait, if there are infinitely many things to narrow down, couldn’t the game take infinitely long? Theoretically, maybe, but in practice, no. This is kind of a paradox. Even though we can conceive of infinitely many things, any particular thing will be guessable in a finite number of questions. After all, the answerer can only reach so far into the infinite depths of the universe before they decide on a thing</i><p>It's probably not like the answerer has access to more than, say, 1M things - I mean as things they can juggle in their mind and pick among.<p>Let's say recording artists: there are 100s of thousands of them globally. But a regular person will perhaps know/recall at best 100-1000 max distinct ones, even if they have heard 2x or 3x others. And they'd be the most likely another would know too.<p>Or let's take numbers: those can be constructed (you don't need to know a number ahead of time to think of it - I can think of 2345324532435245 but I didn't have that in mind as something I've encountered already, I just know that that would be a number, I just need to pile on digits to come up with one). So, yes, this would overflow the "set of items to pick". But "I'm thinking of the specific number X" is not commonly or ever part of the 20 answers game.<p>(Still, if the first N questions make it clear that it's a number that was picked, the next 20 - N ones could try to binary search it).<p>Or let's consider animals and insect: there are 20,000 types of beetles alone. But nobody will put an unknown "beetle type X" (say, "Sitophilus granarius") as the item they think. They'll either think of "beetle" in general, or at best some well known beetle type.<p>One insight is that if the other person doesn't even know of the thing you have in mind, or is not fun guessing it with questions (like a specific huge number), then it makes no sense to pick it, as part of the implicit game rules is for others to have a chance and everybody to have some fun (as opposed to "win at all costs").