Water, poison, and mice

Logic Level pending

There are 3 bottles of water and 1 bottle of clear poison, but you don't know which of the 4 bottles is the poison.

You can mix (or not) the liquids into a serving for a mouse, and any amount of poison will kill a mouse. You have two mice.

What is the fewest number of feedings you need to do to ensure that you can always identify the bottle of poison?

1 4 3 2

5 solutions

Eli Ross Staff
Oct 30, 2015

Mix some liquid from two of the bottles, and feed it to one of the mice.

If the mouse dies, you know that one of those two bottles has poison. Take liquid from exactly one of them and feed it to the other mouse. If it dies, you've found the poison; if it doesn't, the poison is the other of those two bottles.

If the mouse doesn't die, you know that one of the unused two bottles has poison. Take liquid from exactly one of them and feed it to the other mouse. If it dies, you've found the poison; if it doesn't, the poison is the other of those two bottles.

why not mix 1 & 2 and feed it to mouse A, and mix 2 & 3 and feed it to mouse B? If only mouse A dies then poison = 1 if only mouse B dies then poison = 3 if both mice die then poison =2 if no mice die then poison = 4

Nader Khalil - 5 years, 7 months ago

yeah that is a brilliant way and there is much more probability that only one mouse will die .....

Baldev Rinwa - 5 years, 7 months ago

Cool, but isn't it the same probability? Either way, in 2 out of the 4 possible scenarios, one mouse dies; in 1, no mouse dies; and in 1, both mice die.

Dudu Bello - 5 years, 7 months ago

Binary thinking. Most impressive. I like it!

Bobby Lite - 5 years, 7 months ago

Sanjeev, but if the mouse DOES die then there are 3 possibilities. The question is to GUARANTEE you know what it is

Aaren Ruparel - 3 weeks, 6 days ago

No .we can mix three bottles and if the mouse doesn't die the fourth one has the poison so the answer is 1.

Sanjeev Nayak - 5 years, 7 months ago

And what if it dies....

Baldev Rinwa - 5 years, 7 months ago

I thought the same thing, but the question doesn't say "identify a bottle you can drink from", it says "identify the bottle of poison". If the mouse dies, you still don't know which of the three bottles has the poison, although you know the fourth is safe to drink from.

Tim Gallacher - 5 years, 7 months ago

Owen Leong
Nov 2, 2015

Generalization: $\lceil log_{2}(n)\rceil$ , assuming you have n bottles with 1 containing poison.

Vincent Arnel Buerano
Nov 1, 2015

Add a drop of liquid 1 to liquids 2, 3 ,and 4. (Liquid 1+2=mixture 2; 1+3=mixture 3; 1+4=mixture 4;)

Feed mixture 2 to mouse 1. If it dies, then, poison is either liquid 1 or 2 then feed mixture 3 to mouse 2. If it dies, poison is liquid 1. Else, liquid 2 is poison.

If mouse does not die when fed with mixture 2, feed mouse with mixture 3. If it dies, liquid 3 is poison. If it does not, liquid 4 is.

Bot Villegas
Nov 1, 2015

Mix first the 3 bottles...at least you have 75% to get to know the bottle with poison.

Achille 'Gilles'
Nov 1, 2015

Mix a portion of bottle #1 and #2 to a mouse.

Dead mouse? Poison is in #1 or #2. Alive? Poison is in #3 or #4.

Serve a portion from only one bottle in the pair containing the poison, it will identify in which bottle is the poison.

it asks for the fewest # possible...if i feed from 1 bottle only and the mouse dies the answer is 1

kevin m - 5 years, 7 months ago

it asks for the fewest possible number, not the fewest probable number.You must be sure of that number and it can only be 2. Because the probability of finding the poison bottle is 100% if you go for two feedings as mentioned above already by others, but if you go for only a single feeding the probability is only 2/3.

Vishnu S - 5 years, 7 months ago

"it asks for the fewest possible number, not the fewest probable number." if you roll 2 dice in search of a 7 the probability is 1 of 6 however the fewest possible rolls is 1...I stand by my logic. " You must be sure of that number " that part you made up

kevin m - 5 years, 7 months ago

Water, poison, and mice

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