A slightly different version of the puzzle is when the party doesn't start for *two* hours. With one poisoned bottle, how many rats do you need to identify the poisoned bottle with certainty (easy, answer at the bottom of this email). With two poisoned bottles, I have no idea. The question "how many rats do you need to identify both poisoned bottles with certainty" seems to me a more natural problem, and more likely to have an interesting answer, than "what's the best you can do with 10 rats?" Andy On Thu, Nov 15, 2012 at 4:45 PM, Michael Kleber <michael.kleber@gmail.com> wrote:
Hello funsters,
Somehow I've never seen this puzzle before! Is this old hat to any of you?
You have 1000 bottles of wine, which you need for a party that starts in an hour. Two of the bottles are poisoned.
You have ten rats, and you can cause each rat to drink from any subset of the bottles, which will cause it to die if the bottle is poisoned. But the poison takes most of an hour to act, so you only get one round of giving wine to rats, after which you must throw away any bottle which you do not know is safe.
What do you do? I'd be happy to hear either worst-case or average-case results.
Obviously if only one bottle were poisoned, you'd number the bottles and assign one rat to each bit of the binary representation, and the dead rats would spell out the binary of the unique poisoned bottle number. But two poisoned bottles seems to make this much more subtle.
--Michael
-- Forewarned is worth an octopus in the bush. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Solution to the two-hour, one-poisoned-bottle version: 7 rats suffice. Number the bottles in ternary, not in binary. Assign one rat to each position: a zero means the rat doesn't drink from the bottle, a 1 means it drinks from the bottle in the first hour, a two means it drinks from the bottle in the second hour. -- Andy.Latto@pobox.com