Oct 24, 2005
RAY: This is from my chicken-egg series.
TOM: Wait a minute. Can you name any other puzzler that was from the chicken-egg series?
RAY: Uh... no. This is the first. There may have been others. I don't remember. Here it is. It's very simple:
A chicken and a half can lay an egg and a half in a day and a half. How long will it take for two chickens to lay 32 eggs?
TOM: I want to see that half egg!
RAY: I want to see that half chicken!
Here's the question: How long will it take two chickens to lay thirty-two eggs?
RAY: I'm going to tell you how to think about this kind of problem,
so you'll never get stymied again.
If a chicken and a half can lay an egg and a half in a day and a
half, let's double the number of chickens, to three chickens.
Because one and a half chickens laid one and a half eggs, three
chickens laid three eggs in how long?
TOM: In a day and a half.
RAY: Exactly. So if we have three chickens laying three eggs in a
day and a half, then clearly one chicken lays one egg in a day and a
half.
How about two chickens, what do they do? Two chickens lay two eggs.
And two chickens will lay four eggs in three days. So, if two
chickens can lay four eggs in three days, then two chickens can lay
32 eggs in 24 days.
TOM: I think most people are mystified by problems like this.
RAY: Well, I'm glad that for once I was able to demystify. Do we
have a winner?
TOM: The winner this week is Nancy Dorsey from Arlington Heights,
Illinois. And for having her answer selected at random from among
all the correct answers that we got, Nancy is going to get a
26-dollar gift certificate to the Shameless Commerce Division at
cartalk.com. There she can take this gift certificate and get our
spectacular new Car Talk football jersey.
RAY: Berman was wearing it the other day, and three people tackled him.
