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?
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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?
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Fifty One Bicycles
Hint:
The man was playing a poker game and cheated. The bicycles are a type of card. Did you answer this riddle correctly?
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Add Up To 100 Riddle
With the numbers 123456789, make them add up to 100. They must stay in the same order. You can use addition, subtraction, multiplication, and division. Remember, they have to stay in the same order!
Hint:
A Farmer In California
A farmer in California owns a beautiful pear tree. He supplies the fruit to a nearby grocery store. The store owner has called the farmer to see how much fruit is available for him to purchase. The farmer knows that the main trunk has 24 branches. Each branch has exactly 12 boughs and each bough has exactly 6 twigs. Since each twig bears one piece of fruit, how many plums will the farmer be able to deliver?
Hint:
How Many Birth Days Riddle
Hint:
One, he may have many Birthdays, but only one birth day. Did you answer this riddle correctly?
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The Unhappy Cake Riddle
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Making Glass Riddle
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Losing Skin Riddle
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Born In 1957 Riddle
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Three Rivers Riddle
There are three rivers and after each river lies a grave. A man wants to leave the same number of flowers at each grave and be left with none at the end. However, each time he passes through a river, the number of flowers he has doubles. How many flowers does he have to start with so that he is left with none at the end? And how many does he leave at each grave?
Hint:
This problem has an infinite number of solutions modeled by the equation 8a=7n, where a is the amount of flowers the man starts with and n is the number of flowers he leaves at each grave. The simplest and possibly trivial solution would be to start with 0 flowers and leave 0 flowers at each grave. A more significant solution would be to start with 7 flowers and leave 8 at each grave. Any positive integer multiple of this solution also satisfies the conditions. For example, the man starts with 14 flowers and leaves 16 at each grave; so, 14 doubles to 28, and 28-16= 12; 12 doubles to 24, and 24-16= 8; 8 doubles to 16, and 16-16= 0. The result is the same if the man starts with 21 flowers and leaves 24 flowers at each grave, or starts with 28 and leaves 32. Did you answer this riddle correctly?
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The Mountain Of Two Paths
You walk up to a mountain that has two paths. One leads to the other side of the mountain, and the other will get you lost forever. Two twins know the path that leads to the other side. You can ask them only one question. Except! One lies and one tells the truth, and you don't know which is which. So, What do you ask?
Hint:
You ask each twin What would your brother say?. This works because.... Well let's say the correct path is on the left side. So say you asked the liar "What would your brother say?" Well, the liar would know his brother was honest and he would say the left side, but since the liar lies, he would say right. If you asked the honest twin the same question, he would say right, because he knows his brother will lie. Therefore, you would know that the correct path was the left! Did you answer this riddle correctly?
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Tea Cups On The Table
Hint: Try reading the question out loud.
The answer is 3 tea cups because the question was not forty cups it was four tea cups. Did you answer this riddle correctly?
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Wall Clock Riddle
My only timepiece is a wall clock. One day I forgot to wind it and it stopped. I went to visit a friend whose watch is always correct, stayed awhile, and returned home. There I made a simple calculation and set the clock right. How did I do this when I had no watch on me to tell how long it took me to return home from my friends house?
Hint:
Before I left, I wound the wall clock. When I returned, the change in time it showed equaled the time it took to go to my friend's and return, plus the time I spent there. But I knew the latter, because I looked at my friend's watch both when I arrived and when I left. Subtracting the time of the visit from the time I was absent from my house, and dividing by 2, I obtained the time it took me to return home. I added this time to the time my friend's watch showed when I left, and set this sum on my wall clock. Did you answer this riddle correctly?
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Crawling Snail Riddle
A snail was at the bottom of a pole 30 feet tall. It could crawl up 3 feet in one day, but at night it slipped back 2 feet. How long did it take to reach the top of the pole?
Hint:
Twenty-eight days - at the end of the 28th day, it reached the top of the pole, and once on top, of course, it did not slip back down. Did you answer this riddle correctly?
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Pounds Of Sugar Riddle
The grocer had ten customers, each wanting to buy a 2 pound bag of sugar. A 20 pound bag of sugar had been delivered that morning, but he had not yet divided it because he could only find the 5lb and 9lb weights. One of the customers, getting impatient, showed him the quickest way to measure the sugar with the two weights he already had. How did he do it?
Hint:
Weigh out 4 pounds of sugar with the 5lb and the 9lb weights in different pans of the scales. With the 4lb weight , weigh three more lots of 4 pounds each - the remaining sugar will also weigh 4 pounds. Divide each 4 pound portion equally on the two sides of the scales. Did you answer this riddle correctly?
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