You are having a party tomorrow and you’ve bought 13 bottles of wine. You discover one of them is poison. Being the cheapskate that you are, you can’t just dispose of the wine. So, you have these thirteen bottles of wine and one of them contains a poison that will prove fatal within 24 hours after it’s been consumed. You have four small cages, each one containing your standard lab rat. Because the wine takes 24 hours to kill, you can only do one set of tests. So, you have 4 rats in little cages, 13 bottles of wine and one of them has got poison in it. Now you can obviously take samples from any of the bottles and you can give as much or as little as you want to any of the rats. And don’t forget, you’re not going to know if the poison is fatal until the night of the party because it takes 24 hours to kill human or rat. So, how do you do it?

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With 4 rats and one test, we can accomodate up to 16 bottles of wine, using all the combinations of possible dead rats available (=15) + no dead rats (=1)

Solution for 16 bottles:

Bottles from A to P

Rats 1 to 4

Rat 1: A + E + F + G + K + L + M + O

Rat 2: B + E + H + I + K + L + N + O

Rat 3: C + F + H + J + K + M + N + O

Rat 4: D + G + I + J + L + M + N + O

This testing allows each possilbe poisoned bottle to produce a distinguished combination of dead rats

PS: I really hope P is the poisoned one!

Rool and Paul, I really like your answers and both are correct, although explained differently. Here’s how the RiddleDude had it figured:

You need to use a binary numeral system, also called base two.

One, then two, then one and two.

So if you have four rats or four digits, using base two you can create 16 distinct combinations. Here’s how you do it:

Bottle number one goes only to rat one.

Bottle number two goes to rat number two.

Here’s the interesting part. Bottle number three goes to rats one and two. So if rats one and two are belly up the next day, it can only be because bottle number three had the poison in it. If you continue using base two, bottle four goes to rat three and rat three only. Bottle five goes to rats one and three, etc. etc. etc. And each combination corresponds to a different bottle, unique bottle of wine.

Three usable explanations to a tough dilemma.

Congratulations to all!