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I've heard about this interesting cocktail - you get a mug of beer, you drink a sip and refill with vodka. Drink again and refill again. Repeat until there is only vodka in the mug. Then drink and refill with beer until it's only beer in the mug.

So I wondered what the total quantities of beer and vodka would be in the end.

Bobson Dugnutt
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jivko
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    You'd never reach the point of "only vodka in the mug", since you just "diluting" the beer with vodka. The amount of beer in the mug would drop off exponentially, however. – Bobson Dugnutt Oct 19 '17 at 08:07
  • I'm lost at the "Repeat until there is only wodka in the mug". Are you this sure this ever happens? – Mathematician 42 Oct 19 '17 at 08:07
  • Well considering you said "repeat until there is only vodka in the mug" then you've answered your own question. Although in actuality, @Lovsovs is correct. – Andrew Tawfeek Oct 19 '17 at 08:10
  • Try to find a sequence that represents the amount of beer in the mug (perhaps assume that the mug has size 1). Then you will see that it only reaches 0 in the limit (meaning in infinity). – RoyPJ Oct 19 '17 at 08:14
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    That question is unsolvable, at least here in Germany, as no sane person would pollute beer with vodka. – P. Siehr Oct 19 '17 at 08:16
  • In classical physics and assuming the cocktail is properly mixed, with probability $1$ all the molecules would be from the vodka instead of the beer eventually. There is also a simple solution if the sip size is one mug. – Dap Oct 19 '17 at 08:28
  • If we take account the fact that matter consists of particles, it would end in finite time almost surely. For instance, assuming that there are $10^{25}$ particles in the initial mug of beer and every sip is $1%$ of the total volume of the liquor in the mug, heuristic computation (either by geometric sequence or by the coupon collector problem) tells that we need roughly $5800$ sips (i.e. $58$ mugs) in average to drink out all the particles of the initial beer. – Sangchul Lee Oct 19 '17 at 08:29
  • @SangchulLee: sounds like an answer! – Dap Oct 19 '17 at 08:37
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    @PhilippSiehr Perfectly solvable in Russia ;) – Evgeny Oct 19 '17 at 08:38
  • Well, not the answers I expected but they made me laugh :) Thanks all! – jivko Oct 20 '17 at 03:06
  • This question is only practically (if u know what I mean) solvable. If you want to pen it down, then its impossible. – geeky me Oct 22 '17 at 18:09

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