But what information does he use to deduce that 1 and 2 must have a beer?
If all 3 enter into the joke in the "not-knowing" state [ 0 0 0 ]
then through the dialogue, information must be imparted to make it [ 0 0 1 ]
but they say "I don't know"
which afaict doesn't give 3 any information to make a deduction.
(not to over-intellectualize your joke or anything)
sorry
that set is [ 0 0 1 ] already
since 3 knows whether he want a beer or not,
but he needs to determine which of the other four possible configurations exist.
If [0 y z] then 1 would be able to say no on his turn, since him being 0 is sufficient to reply to question that way (he knows at least one person, himself, will not have beer). If [1 y z] he would not know for sure. Thus we know it's 1 for him on turn 2.
Similarly for 2.
So three knows it's [1 1 z], and we learn he also wants a beer when he answers yes.
The side joke I shared is actually more clear on some respects, if that helps (even though was meant as insult to npub Techno).
Hope that helps
