Bottle

(In English please)

Megha said:



fresco said:



I say:

My friendly local apothecary has offered me at least 15 assorted bottles, phials and flacons containing his finest. One of the vials contains the vilest deadly poison. I have amazed a group of 4 rats. How do I find the bottle containing the poison with their inadvertent assistance?

Clue: The pellet with the poison's in the flagon with the dragon; the vessel with the pestle has the brew that is true.

hehehe....

Is anyone here able to answer the question?

15 bottles, 4 rats, which bottle contains the poison?

It looks like a variation of the minimum number of scale pan weighings problem for 12 balls. I suppose you set up samples of mixture from 5 bottles at a time and on finding the lethal sample do 2 against 2 etc. (The twelve ball problem is a lot harder with scale pan switching to find the odd one out)

Number the rats 1, 2, 4, 8. Number the bottles 1-15. On each bottle, write the bottle number as the sum of unique powers of two (e.g. 11 = 1+2+8).

Each rat will get a mixture which consists of liquid from all of the bottles with the rat's number in the sum expression (e.g. rat 4 will get liquid from bottles 4, 5, 6, 7, 12, 13, 14, 15).

After the rat(s) has/have died, add their numbers to get the bottle number that contains the poison.

Give first rat mixture from bottles 1 - 5
If rat dies, give second rat mixture 1+2. (If it lives give 3+4... etc)
If rat dies give third rat bottle 1 hence answer 1 or 2

If bottles 1-5 keep rat alive, give first rat mixture 6-10 ( or 11-15)
and repeat logic of "halving" as above.

This method has the "advantage" of economy of 3 rat maximum usage .

(This method is an adaptation of the "12 ball minimum balance pan weighings" problem in which the balls are identical except for the weight of one of them)

Rats. For one wonderful moment I wondered whether or not the rats had a solution.

I prefer the elegance of painting the rats with a non-toxic solution al a markr pencilled fresco. The same number of rats are imperilled in either scenario if you are patient.

My money is on the mystery bottle 16.

Thank you chai. Tea for 2?

I believe the original problem I'm familiar with had a time constraint, and it took a while for the poison to kill. In that case a sequential procedure would not be completed in time. It can be solved with a single rat if you feed it from one bottle at a time.