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?

With 9 testers, you would need to number the bottles starting with 1, as you need at least one death on day 7 to correctly identify the tenth bit position.

This is not true for the second group, since if no-one dies on day 7 you know the tenth bit was set, and then if no tester dies on day 8 you know it was specifically the bottle with only the tenth bit set.

Posted by vertigo on 2005-02-26 19:15:02