The Last Seat : Car Talk Puzzler

Yet another great car talk puzzler, The Last Seat:

RAY: You’re one of a hundred people standing in line to get onto an airplane that has 100 seats. There’s a seat for every person who’s in line, and each of you has a boarding pass for your assigned a seat. The first person to walk onto the plane drops his boarding pass and, instead of picking it up, decides, “I’m just going to sit anyplace.” He takes a seat at random.

Now, every other passenger will take either his assigned seat or, if that seat is taken, that passenger will take any seat at random.

TOM: I’ve been on that flight!

RAY: You are the last passenger to walk onto the plane. Obviously, there’s going to be one seat left, because everyone else is sitting in his correct seat, or not.

The question is: What are the chances that you get to sit in your assigned seat? I’m going make this multiple choice.

A: 1 out of 2.
B: 1 out of 10.
C: 2 out of 50.
D: 1 out of 100
E: Zero.

What strategies could you give students to help them reason their way through this puzzle?

2 thoughts on “The Last Seat : Car Talk Puzzler

  1. Since it’s about 100 years ago I last looked at this sort of slightly annoying (!) problem I found myself in the position of your students. My suggested strategy is “Read the question, and now read between the lines, and now read the mind of he who thought this one up.”

  2. I’d suggest that they take a look at this scenario with just two passengers. Then three. And four. And so on. Notice any patterns?

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