Tire mounting... with but a few letters

Oct 09, 2006

RAY: I had to re-obfuscate this. I thought Sue Olster did a pretty good job, but I think I did a better job. We'll see.

She wrote the following:

I'm going to have winter tires put on my car. I bought four of them. I'm moving soon, and since I'll be taking the car to a different shop to have them changed back next spring, the tires have to be marked so they can be put back where they belong, i.e., where they came from. So the left front has to go the left front, the right front has to go there, and so on.

When I take them off, I'm going to ask the people at the gas station to mark them with letters.

The question is, what's the smallest number of letters needed to mark my tires to guarrantee that all four of them can get correctly installed with no chance of error or ambiguity in the spring?
Answer: 
RAY: The answer is two. Two letters and each is used twice. The two letters are L and F.

Here's how the tires would be marked. By the way, you could do this different ways, and you could use different letters, but this works.

The left front tire would be marked LF. The other front tire would simply be marked F.

The left rear tire would just be marked L.

TOM: And the fourth tire, which is the right rear, wouldn't be marked at all.

RAY: Right. Two letters, each of which is used twice. Do we have a winner?

TOM: Yeah, we have a winner. The winner is Ted Shaft from Proctor, Vermont, and for having his answer selected at random from among all the correct answers that we actually got, Ted is going to get a 26-dollar gift certificate to the Shameless Commerce Division at cartalk.com with which he can get our brand-new CD called, Once Upon a Car Fire, The Greatest Stories Ever Told.

RAY: This is a collection of stories, mostly embarrassing stories I guess, but all funny stories about stuff that has happened to us over the years.

TOM: And it's not just happened to us, it's also friends, relatives, staff members.

RAY: Oh yeah, none of them are talking to us anymore.

TOM: No.

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