Part 1:
1)A king knows he's going to die and decides to leave all his wealth to the most intelligent of his three sons. So he tells them that he's going to put them through a test, and the first person to give the correct answer would get it all.
He tells his sons:
1. I'll seat the three of you in a room such that each person can see the other.
2. On each of your heads, I'll put a cap, the colour of which will be either blue or black...each person will be able to see the colour of the cap on the other two people, but will obviously not be able see the colour of the cap on his own head.
3. The moment someone sees 2 black caps and 2 black caps only, he raises his hand to give a signal.
4. You have to correctly work out the colour of the cap on your own head.
So saying, he seats them in the room and puts a blue cap on each one's head. Naturally, no one gives a signal because no one can see two black caps (each can see two blue caps on the others' heads obviously). However, after a couple of minutes, the most intelligent son correctly says that a blue cap is on his head and thus gets all the wealth.
Question: How does he work it out??
2)
A king is about to have a celebration tommorrow. The celebration is the most important party he has ever hosted. He has got 1000 bottles of wine for the celebration, but he has just got to know that one of them is poisoned.
The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison. The king has just 10 prisoners at his disposal (to sacrifice if need be) and just under 24 hours to determine which single bottle is poisoned. How does the king find the poisoned bottle by using just these 10 prisoners?
3)
A mad king tells his 100 wisest men he is about to line them up and place either a red or blue hat on each head. Once lined up, they must not communicate amongst themselves nor attempt to look behind them nor remove their own hat.
The king tells the wise men that they will be able to see all the hats in front of them. They will not be able to see the color of their own hat or the hats behind them, although they will be able to hear the answers from all those behind them.
The king will then start with the wise man in the back and ask "what color is your hat?" The wise man will only be allowed to answer "red" or "blue," nothing more. If the answer is incorrect then the wise man will be silently killed. If the answer is correct then the wise man may live but must remain absolutely silent.
The king will then move on to the next wise man and repeat the question.
Before they are lined up, the king makes it clear that if anyone breaks the rules then all the wise men will die. The king listens in while the wise men consult each other to make sure they don't devise a plan to communicate anything more than their guess of red or blue.
The wise men devise a method in which a maximum on only 1 wise man need be killed. What method do they use?
4)
1000 people are standing in a circle...the first person has a gun.he kills the person next to him and passes the gun to the third person. The third person kills the person next to him and hands over the gun to the fifth person. This continues until there is just one person left alive
who will be the last person left alive..??
5)A jail warden meets with 23 new prisoners when they arrive and tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another."
"In the prison is a switch room, which contains two light switches labeled 1 and 2, each of which can be in either up or the down position. I am not telling you their present positions. The switches are currently not connected to anything."
"After today, from time to time, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell."
"No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back. I will not touch the switches myself."
"Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone may declare to me, 'We have all visited the switch room.'"
"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you"
What is the strategy they come up with so that they can be free?
- You have to get from point A to point B. You don’t know if you can get there. What would you do?
- Imagine you have a closet full of shirts. It’s very hard to find a shirt. So what can you do to organize your shirts for easy retrieval?
- What method would you use to look up a word in a dictionary?
- Every man in a village of 100 married couples has cheated on his wife. Every wife in the village instantly knows when a man other than her husband has cheated, but does not know when her own husband has. The village has a law that does not allow for adultery. Any wife who can prove that her husband is unfaithful must kill him that very day. The women of the village would never disobey this law. One day, the queen of the village visits and announce that at least one husband has been unfaithful. How many husbands get killed; if any; & in how many days ??
- Mike has $20 more than Todd. How much does each have given that combined they have $21 between them. You can’t use fractions in the answer.
- How do you cut a rectangular cake into two equal pieces when someone has already taken a rectangular piece from it? The removed piece an be any size or at any place in the cake. You are only allowed one straight cut.
- How many piano tuners are there in the entire world?
- Two MIT math graduates bump into each other. They hadn’t seen each other in over 20 years.The first grad says to the second: “how have you been?” Second: “Great! I got married and I have three daughters now” First: “Really? how old are they?” Second: “Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..” First: “Right, ok.. oh wait.. I still don’t know” second: “Oh sorry, the oldest one just started to play the piano”First: “Wonderful! my oldest is the same age!” So, how old are the daughters?
- What gives you joy?
- Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it’s only strong enough to support two people at any given time. Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?
- If the probability of observing a car in 30 minutes on a highway is 0.95, what is the probability of observing a car in 10 minutes (assuming constant default probability)?
- In a country in which people only want boys, every family continues to have children until they have a boy. if they have a girl, they have another child. if they have a boy, they stop. what is the proportion of boys to girls in the country?
- You have an empty room, and a group of people waiting outside the room. At each step, you may either get one person into the room, or get one out. Can you make subsequent steps, so that every possible combination of people is achieved exactly once?
- You are at a party with a friend and 10 people are present including you and the friend. your friend makes you a wager that for every person you find that has the same birthday as you, you get $1; for every person he finds that does not have the same birthday as you, he gets $2. would you accept the wager?
- How many golf balls can fit in a school bus?
- You are shrunk to the height of a nickel and your mass is proportionally reduced so as to maintain your original density. You are then thrown into an empty glass blender. The blades will start moving in 60 seconds. What do you do?
- How much should you charge to wash all the windows in Seattle?
- How would you find out if a machine’s stack grows up or down in memory?
- Explain a database in three words to your eight-year-old nephew.
- You have five pirates, ranked from 5 to 1 in descending order. The top pirate has the right to propose how 100 gold coins should be divided among them. But the others get to vote on his plan, and if fewer than half agree with him, he gets killed. How should he allocate the gold in order to maximize his share but live to enjoy it?
- In a country in which people only want boys, every family continues to have children until they have a boy. if they have a girl, they have another child. if they have a boy, they stop. what is the proportion of boys to girls in the country?
1)A king knows he's going to die and decides to leave all his wealth to the most intelligent of his three sons. So he tells them that he's going to put them through a test, and the first person to give the correct answer would get it all.
He tells his sons:
1. I'll seat the three of you in a room such that each person can see the other.
2. On each of your heads, I'll put a cap, the colour of which will be either blue or black...each person will be able to see the colour of the cap on the other two people, but will obviously not be able see the colour of the cap on his own head.
3. The moment someone sees 2 black caps and 2 black caps only, he raises his hand to give a signal.
4. You have to correctly work out the colour of the cap on your own head.
So saying, he seats them in the room and puts a blue cap on each one's head. Naturally, no one gives a signal because no one can see two black caps (each can see two blue caps on the others' heads obviously). However, after a couple of minutes, the most intelligent son correctly says that a blue cap is on his head and thus gets all the wealth.
Question: How does he work it out??
2)
A king is about to have a celebration tommorrow. The celebration is the most important party he has ever hosted. He has got 1000 bottles of wine for the celebration, but he has just got to know that one of them is poisoned.
The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison. The king has just 10 prisoners at his disposal (to sacrifice if need be) and just under 24 hours to determine which single bottle is poisoned. How does the king find the poisoned bottle by using just these 10 prisoners?
3)
A mad king tells his 100 wisest men he is about to line them up and place either a red or blue hat on each head. Once lined up, they must not communicate amongst themselves nor attempt to look behind them nor remove their own hat.
The king tells the wise men that they will be able to see all the hats in front of them. They will not be able to see the color of their own hat or the hats behind them, although they will be able to hear the answers from all those behind them.
The king will then start with the wise man in the back and ask "what color is your hat?" The wise man will only be allowed to answer "red" or "blue," nothing more. If the answer is incorrect then the wise man will be silently killed. If the answer is correct then the wise man may live but must remain absolutely silent.
The king will then move on to the next wise man and repeat the question.
Before they are lined up, the king makes it clear that if anyone breaks the rules then all the wise men will die. The king listens in while the wise men consult each other to make sure they don't devise a plan to communicate anything more than their guess of red or blue.
The wise men devise a method in which a maximum on only 1 wise man need be killed. What method do they use?
4)
1000 people are standing in a circle...the first person has a gun.he kills the person next to him and passes the gun to the third person. The third person kills the person next to him and hands over the gun to the fifth person. This continues until there is just one person left alive
who will be the last person left alive..??
5)A jail warden meets with 23 new prisoners when they arrive and tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another."
"In the prison is a switch room, which contains two light switches labeled 1 and 2, each of which can be in either up or the down position. I am not telling you their present positions. The switches are currently not connected to anything."
"After today, from time to time, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell."
"No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back. I will not touch the switches myself."
"Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone may declare to me, 'We have all visited the switch room.'"
"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you"
What is the strategy they come up with so that they can be free?
***** mail me at CrazyEmperor.com@gmail.com for the answers *****
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