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?

Divide bottles by 11!!!  91 apiece; the remaining 90 are given day 2 only 9 drink each (9 not yet touched).  Day 3 8 of the remaining 9 are sipped (1 not).  By the End of day #7, beginning of day #8 either someone dies or you wait until tomorrow. 

    If someone dies on day #7, then the deceased testers 91 bottles would be divied up 10 ways accross the 9 remaining testers (9each).  Each of the 9 bottles laid then to rest would be consumed the following day 1 each in which case a second, case solving death will occur by the end of day 15 or 16.

    If however no one dies on day #7, and someone dies from day#2's wine, those 9 bottles would again be drunk 1 each by the remaining 9, for 2 deaths.

    Otherwise you know by the end of day #9 which bottle it was with either 1 or 0 (if it was the bottle that was forever untouched).

Posted by Douglas on 2005-03-31 09:06:42