Pickett

I heard this one a long time ago...and it probably would help to have said they were stranded on an island for a long time...but given that: Or some variation on that...

Haha, that's kind of fun to wrap your head around...

well...

Depends...

...a lot...

@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.

Approach

Yes...I can.

FWIW

Nevermind...misunderstood the OP (again).

I assumed my answer was along the right lines, but I was too lazy to actually find the true minimum with it...thanks for doing the dirty work!

How about

My brain isn't exactly firing on all cylinders today, but...

I got

How about

I've not heard this one...but I'll take a stab:

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 however many tokens as they want)? So, if that's the case, it becomes a much more challenging problem. Obviously it doesn't make sense to purchase more than 9 tokens, as with 10 the BEST you could hope for is breaking even...I would probably purchase the following numbers (and my rationale next to them): 1 - I'm assuming I will lose this $10, but maybe everyone else will think someone else picks this and therefore no one else does! 2 - Might as well try this one as well, but again, most likely will lose this $10 as well... 7...ish - Some relatively low number that hopefully no one else picks...I would assume I'd lose this. 10 - Let's assume everyone buys their 9 tokens and picks 1-9...10 would be the first number that no one would pick... 16...ish - Again, some pretty low number, that's pretty much just a shot in the dark and you hope no one else picks it. 42 - If by some crazy chance everyone buys 9 tokens and all are duplicated, this is the lowest possible number that wouldn't be duplicated...plus isn't it really the answer to everything? At this point, I've already bet $60 in hopes of winning $100...and really, the odds are still not in my favor...so to me, it's not worth the risk and so my ultimate strategy would be to not play and "break even" :c)