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