kimblanchard Posted October 13, 2004 Share Posted October 13, 2004 The puzzler from Car Talk was very interesting this week. You are the last guy in line to get on an airplane. There are 100 people in line, and 100 seats. Each of you have a boarding pass directing you to a particular seat. As the first guy is getting on the plane, he drops his boarding pass, and rather than stop to pick it up, he just goes and sits on the plane somewhere. The rest of the people will go sit in their seat unless someone is already there. If someone is in their seat, they will sit in any one of the remaining seats at random. When you walk onto the plane, there will be one seat left. What is the probability that it is the seat on your boarding pass? Hint, try working it out if there are 2, 3, or 4 people and seats. Then maybe you can visualize the pattern. I will come back with the answer after linear algebra. Which should be about 7 central. Curtis Quote Link to comment Share on other sites More sharing options...
cindi o'h Posted October 13, 2004 Share Posted October 13, 2004 okay, Curtis. Again, I am like........Huh??? Cindi o'houlighan Quote Link to comment Share on other sites More sharing options...
kimblanchard Posted October 13, 2004 Author Share Posted October 13, 2004 Say there are 3 seats instead of 100. The first guy walks in without a ticket. He could either sit in seat one (his seat) seat two (the other guy's seat) or seat three (your seat). If seat 2 is available, then guy 2 will always sit there because he has his ticket and the correct seat is available. If someone is in seat 2, then he will choose between seat one and seat three. When you walk in, you take whatever seat is left. What is the probability that it is the actual seat you are supposed to have? When you have figured it out for two or three or four people, you should be able to figure it out for 100. What is the probability you end up in seat 100? That is the question. Curtis Quote Link to comment Share on other sites More sharing options...
cindi o'h Posted October 13, 2004 Share Posted October 13, 2004 Okay, Curtis.. I am still like......huh? I mean I am still trying to figure out why in the world I would be the last guy on the flight....I am always just about first in line. And why would some guy drop his boarding pass and still be able to get on the flight? And, where are we going anyway? And is the lounge open? Is there bar service? And who is going to be serving me. That's all I am saying.....I am still working out the details, that's all... Cindi o'houlighan Quote Link to comment Share on other sites More sharing options...
Debi Posted October 14, 2004 Share Posted October 14, 2004 Okay Curtis..I don't even have friggin indoor lectricity or plumbin' and you want me to figure out one of them thar fancy mathematical equasions??? Quote Link to comment Share on other sites More sharing options...
cindi o'h Posted October 14, 2004 Share Posted October 14, 2004 okay, Curtis, my pencil is all chewed up...I got teeth marks all over it and the eraser is half chewed off and spit out... If I were the last "guy" on the flight, I would sqirm ahead of someone who is busy putting their carry on luggage in the overhead. Then I wouldn't have to think about probabilities...... Is that the right answer? Or should I have picked up that guy's boarding pass and used his seat? What if his seat was next to the toidies? I wouldn't want to sit there! Is that the right answer? I'm sure I got lead poisoning now....dangit. Cindi o'houlighan Quote Link to comment Share on other sites More sharing options...
kimblanchard Posted October 14, 2004 Author Share Posted October 14, 2004 I like Cindy's answer, but I am a math guy. The answer is there is a 50/50 shot you will end up in your assigned seat. Here is the reasoning. The first guy on who dropped his pass - I know he is an idiot - can do one of three things. If he sits in his seat, then everyone will sit in their correct seat including you. If he sits in your seat, everyone will sit in their correct seat except for him and you. The rest of the time, he will sit in someone else's seat. And the number of the seat will be higher than one. Let's say the first guy sits in number 2's seat. Then when number two sits down, he will do one of three things: he could sit in 1's seat, he could sit in your seat, or he could pass the decision on to someone else by sitting in their seat. Say he sits in #99's seat. Then the rest of the people get on, except for #99 and you. And there are just two seats left: #1 and #100 (yours). If he sits in your seat, you sit in #1's. If not, he sits in #1 and you sit in your seat. So at each step of the process - there is a 50/50 shot the game will be ended by you sitting in your seat or #1's, or the decision will be passed to someone with a higher number. Therefore, there is a 50% chance you will sit in your seat when you get on board. Pretty cool? Curtis Quote Link to comment Share on other sites More sharing options...
cindi o'h Posted October 14, 2004 Share Posted October 14, 2004 oh...that's what you were talking about. well, in that case, the answer was easy. Iknewthat. cindi o'h Quote Link to comment Share on other sites More sharing options...
draiocht_bean_si Posted October 14, 2004 Share Posted October 14, 2004 no fair i just saw it do another please Quote Link to comment Share on other sites More sharing options...
Frank Lamb Posted October 14, 2004 Share Posted October 14, 2004 Well Done Curtis,that was a real stumble bumbler. Quote Link to comment Share on other sites More sharing options...
Snowflake Posted October 14, 2004 Share Posted October 14, 2004 Curtis, Knowing how tall you are, even if you WERE the last man on, you STILL wouldn't be joining the mile-high club! It's all fun and games until someone gets hurt.....and trying to fit two folks in the potty would leave to someone getting hurt... Becky Quote Link to comment Share on other sites More sharing options...
teresag Posted October 15, 2004 Share Posted October 15, 2004 I'm trying this out without reading the other posts so I can mess it up without any help. But I need more information. Was the seat the first guy was originally assigned a middle seat? That would drastically reduce the chances that he'd choose the correct seat without looking at his boarding pass. If it was an aisle seat on the exit row, then his chances of choosing correctly are greater. Or are we simply assuming that this does not enter into the equation and that he chooses a seat at random from the 100 choices? I'm a veteran of Car Talk trivia, ya know....back when they had online trivia a few years ago. So I know how bogus Click and Clack-style questions can be. Quote Link to comment Share on other sites More sharing options...
kimblanchard Posted October 15, 2004 Author Share Posted October 15, 2004 All of the seats are equally unappealling. So the first guy (and anybody else whose seat is taken, for that matter) will sit in any seat at random. Curtis Quote Link to comment Share on other sites More sharing options...
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