The 100 Seat Airplane
People are waiting in line to board a 100-seat airplane. Steve is the first person in the line. He gets on the plane but suddenly can't remember what his seat number is, so he picks a seat at random. After that, each person who gets on the plane sits in their assigned seat if it's available, otherwise they will choose an open seat at random to sit in.
The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?
The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?
Hint: You don't need to use complex math to solve this riddle. Consider these two questions:
What happens if somebody sits in your seat?
What happens if somebody sits in Steve's assigned seat?
The correct answer is 1/2.
The chase that the first person in line takes your seat is equal to the chance that he takes his own seat. If he takes his own seat initially then you have a 100% chance of sitting in your seat, if he takes your seat you have a 0 percent chance. Now after the first person has picked a seat, the second person will enter the plan and, if the first person has sat in his seat, he will pick randomly, and again, the chance that he picks your seat is equal to the chance he picks someone your seat. The motion will continue until someone sits in the first persons seat, at this point the remaining people standing in line which each be able to sit in their own seats. Well how does that probability look in equation form? (2/100) * 50% + (98/100) * ( (2/98) * 50% + (96/98) * ( (2/96) * (50%) +... (2/2) * (50%) ) ) This expansion reduces to 1/2.
An easy way to see this is trying the problem with a 3 or 4 person scenario (pretend its a car). Both scenarios have probabilities of 1/2. Did you answer this riddle correctly?
YES NO
The chase that the first person in line takes your seat is equal to the chance that he takes his own seat. If he takes his own seat initially then you have a 100% chance of sitting in your seat, if he takes your seat you have a 0 percent chance. Now after the first person has picked a seat, the second person will enter the plan and, if the first person has sat in his seat, he will pick randomly, and again, the chance that he picks your seat is equal to the chance he picks someone your seat. The motion will continue until someone sits in the first persons seat, at this point the remaining people standing in line which each be able to sit in their own seats. Well how does that probability look in equation form? (2/100) * 50% + (98/100) * ( (2/98) * 50% + (96/98) * ( (2/96) * (50%) +... (2/2) * (50%) ) ) This expansion reduces to 1/2.
An easy way to see this is trying the problem with a 3 or 4 person scenario (pretend its a car). Both scenarios have probabilities of 1/2. Did you answer this riddle correctly?
YES NO
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I have rivers, but don't have water. I have dense forests, but no trees and animals. I have cities, but no people live in those cities. What am I?
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I can open a place or close empty space; show you behind to put a smile on your face. I am both figurative and literal, solid or thought- to choose to enter, or to think nought. I'm a gateway that you pass through everyday- though you forget how I affect the path that you stay. For, though the scenes change and turn into dreams, I am a constant with you, forever it seems.
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100 Politicians Riddle
There is a party of 100 high-powered politicians. All of them are either honest or liars. You walk in knowing two things:
- At least one of them is honest.
- If you take any two politicians, at least one of them is a liar.
From this information, can you know how many are liars and how many are honest?
- At least one of them is honest.
- If you take any two politicians, at least one of them is a liar.
From this information, can you know how many are liars and how many are honest?
Hint:
Yes, from the information you know 1 is honest and 99 are liars.
One of them is honest satisfying the first piece of information. Then if you take the honest man and any other politician, the other politician must be a liar to satisfy the second piece of information, 'If you take any two politicians, at least one of them is a liar.' So 99 are liars. Did you answer this riddle correctly?
YES NO
One of them is honest satisfying the first piece of information. Then if you take the honest man and any other politician, the other politician must be a liar to satisfy the second piece of information, 'If you take any two politicians, at least one of them is a liar.' So 99 are liars. Did you answer this riddle correctly?
YES NO
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