@Cygnet I think something is wrong with your solution, as one of the requirements is that "18 of us did not drink water."
by your answer, you have 8 that drank nothing, 7 that drank only wine, and 11 that drank beer and wine...which totals 26 people that did not drink water.

I'm guessing it's because I missed this piece of the assumption: "who drank beer and water but not wine were as many as possible".
I'll give it another go with the non-drinkers included and that piece and see what I come up with.

I guess I took this question to be something different. Rather than just "what's the smallest positive value you can think of?" for which I would go with something like:
1-(3↑↑↑↑...↑↑3)
or in other words: 1 over Graham's number (or simply "G")...but why stop there? why not go with
1/G↑↑↑↑↑↑↑...↑↑↑↑↑↑↑↑G
That interpretation of the OP isn't as interesting or fun because it just gets ridiculous... The way I took the original question was pick the smallest positive INTEGER that no one else picks...what is your strategy when up against 9 others doing the same (all allowed to pick ho