There are 1000 bottles of wine and you know that there is exactly one of them that is poisonous, and will kill the drinker in 7 days. (To be precise, it will take randomly from 7 days to 7 days 23 hr 59 min 59 sec.) Now you have 10 testers who are willing to risk their lives and test-drink those wines. What is the smallest number of days you need to figure out which bottle contains the poisonous wine? In addition, under this strategy, what is the maximum and minimum number of deaths? The extension to this problem is, how will your strategy change if you only have 9 testers?

There is a trick I have seen where you ask your 'victim' to choose a number between 1 and 64, without telling you what it is. Then you hand them a stack of numbered cards, and they must give you the cards on which their number appears. They do this, and you immediately tell them what number they thought of.

It works on the same principle, and I dare say had I never seen that game I would have found this puzzle more difficult. In the card game, each card carries numbers with a specific bit set, and the cards they give correspond in the same way as the dead testers tell you which wine bottle was poisonous.

Posted by vertigo on 2005-02-26 19:33:31