One Seat Left. Is It Yours?

The Puzzler

RAY: I made it multiple-choice. And the options were A) one out of two, B) one out of ten, C) two out of 50, which happens to be one out 25, D) one out of 100, and E, zero.

Now our guy with the lost boarding pass, he could by dumb luck wind up in his assigned seat, right?

TOM: He could.

RAY: In which case each subsequent passenger including me, if I'm the last person, will get the right seat.

But what's more likely is that he takes someone else's seat. It's much more likely.

Now, here's the counterintuitive part. There are only two seats that count, my seat and his seat. All the other seats don't make a difference. Whoever gets on the plane subsequent to him, those people are going to take some seat or another.

Nothing matters until either my seat gets taken or his seat gets taken. If my seat gets taken by some displaced passenger, then I have zero chance of getting my seat.

Are you with me?

TOM: I'm with you.

RAY: If his seat gets taken by some displaced passenger then every other passenger who walks onto the plane including me, will have his assigned seat.

And how often does that happen? One time out of two. Half the time my seat's going to get taken by some displaced passenger, and half the time his seat is going to get taken by a displaced passenger.

TOM: So your chances are A) one out of two.

RAY: 50/50. Hard to believe! Do we have a winner?

TOM: We do. The winner this week is Eliot Gazanski from Ann Arbor, Michigan. And for having his answer selected at random from the thousands of correct answers that we got, Eliot will win a $26 gift certificate to the Shameless Commerce Division at where he can get among other things a distressed Car Talk T-shirt. And trust me you will look distressed when you're wearing it, Eliot.

[ Car Talk Puzzler ]

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