Revolt of the Lab Rats

Feb 15, 2010

RAY: This was from my 'revolt of the lab rats' series and it was sent in interestingly enough by a fellow named Andrew Magliozzi, who happens to be my son! I thought the name looked familiar.

Imagine this: It's the eve of the annual Car Talk 'We Haven't Been Canceled Yet' Banquet. John 'Bugsy' Lawlor has procured the food and the wine for the following evening's gala, and he's extremely pleased with himself because he knows a guy, who knows a guy, who knows a guy, and he's obtained for $50, thirteen one-half gallon jugs of the finest red wine. He's very excited about the following evening's festivities until Doug 'Punkin Lips' Berman informs him that he received a note suggesting that one of those 13 bottles of wine contains a deadly poison. In fact, it's one that kills within 24 hours. 'Is someone out to get us? Who could be out to get us? Why? Why not? But why the whole staff?'

Anyway, because they're hopeless cheapskates and unwilling to discard 12 bottles of perfectly good cheap wine, they head off to MIT to consult with a scientist friend of theirs. 'So let's see,' he says, '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. And the Car Talk Extravaganza is when?'

'Tomorrow night.'

The scientist goes on to suggest that from his knowledge of poisons, even the smallest sample is usually enough to cause certain death, even if mixed and diluted with the wine from the untainted bottles. 'Hmm,' he says, 'I'll be right back.'

In a flash, he returns with four small cages, each one containing your standard lab rat. What a moral dilemma, they think, we have to sacrifice lab rats to save Car Talk? 'But wait, wait,' they say. 'We have 13 bottles of wine. How are we supposed to save the entire Car Talk staff and empire, with just 4 rats?'

'You can do it,' he says and then disappears into the inky shadows.

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 banquet because it takes 24 hours to kill human or rat. So, how do you do it?
Answer: 

RAY: Here's the answer. You use base two.

TOM: Oh, that's right. One, then two, then one and two.

RAY: Exactly. 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.

TOM: Oh, very good.

RAY: And 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.

It's very cute and our web lackeys made a nice visual explanation of the answer on our website and it's a lot easier to understand if you can see the drunken rats. So who's our winner?

TOM: Our winner this week is Helen Nye from Montclair, New Jersey. And for having her answer selected at random from among all the correct answers that we got, Helen's going to get a 26 dollar gift certificate to the shameless commerce division at Car Talk dot com. With which she can get a copy of our latest CD, Tales of the Brothers Grime.

RAY: Congratulations Helen!

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