Tea and coffee problem

Just test the Random label. If it vends coffee, you know it is the Coffee container (it cannot be Random, as the label is wrong, and it obviously isn't Tea.) Knowing this, you know that the Tea label must be the Random container (it cannot be Coffee as that is already taken, and it cannot be Tea because the label must be wrong.) And, of course, the Coffee label must be Tea by elimination.

Similarly, if the Random label vends tea, you know it is the tea container. This means that the Coffee label must be the random container (it cannot be coffee and tea is already taken) and therefore the Tea label must be coffee.

The interesting thing is that there are only 2 possible permutations where all three labels are wrong. Note that testing either the Coffee or Tea label first may require two tests, not just one, as there in not enough information contained in the result if the beverage delivered does not match the label. If it does match the label, you can also solve as above, knowing the tested container is the Random container.

It is stated that each label is incorrect, so pressing random immediately tells you which is either only coffee or only tea, the label saying the other beverage of the two will be random since it is also incorrect, and the last one will be the remaining unlabeled drink

Re: some confusion below; A better version of this puzzle comes from Martin Gardner; three boxes are labeled "Apples" , "Oranges" and "Apples and Oranges". Thus taking a single piece of fruit from this last box yields the solution. I think the use of the label "Random" in the drinks version is the reason for the consternation!

Answer is one try!!!! you should just try "random" labeled one! That gives you a tea or a coffee.... if its a tea then "coffee" labeled one should be the "true random" one and the "tea" labeled one should be the "true coffee". Otherwise ... you get the coffee from the "random" one then the "tea" labeled one should be the "true random" and the "coffee" one should be the "true tea" :)

In the first turn you check all the buttons and you may got the follow results:either 2 buttons have given you coffee or 2 buttons have given you tea.Let´s say 2 of the buttons have given you tea.This means that of those is the random button.The button that has given you coffee must be labeled as either tea or random.The both button that have given you tea must to be labeled as either coffee or random.As the random cannot be labeled as random,if one of those buttons which has given you tea be labeled as tea you may realize that´s the random one.And if the coffee button is labeled as tea,then the random must be labeled as coffee.

It has been specified in the question that "these three labels have been mixed up such that they all describe one of the other drinks". So, in the dispenser marked "tea" will give either coffee or random. But it cannot give tea. Hence, it will only give coffee. Similarly, the one marked "coffee" will give tea. The one marked "random" can give any of the two drinks. Therefore we can dispense the label which is marked "tea" or the one marked "coffee". '1' is the correct option.