## Thursday, April 15, 2010

### 100 Prisoners in Solitary Cells

100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say “Every prisoner has been in the special room at least once”. If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?

### Apples and Oranges?

You have 3 baskets, one with apples, one with oranges and one with both apples and oranges mixed. Each basket is closed and is labeled with ‘Apples’, ‘Oranges’ and ‘Apples and Oranges’. However, each of these labels is always placed incorrectly. How would you pick only one fruit from a basket to place the labels correctly on all the baskets?

### 5 Pirates Fight for 100 Gold Coins

Five pirates discover a chest containing 100 gold coins. They decide to sit down and devise a distribution strategy. The pirates are ranked based on their experience (Pirate 1 to Pirate 5, where Pirate 5 is the most experienced). The most experienced pirate gets to propose a plan and then all the pirates vote on it. If at least half of the pirates agree on the plan, the gold is split according to the proposal. If not, the most experienced pirate is thrown off the ship and this process continues with the remaining pirates until a proposal is accepted. The first priority of the pirates is to stay alive and second to maximize the gold they get. Pirate 5 devises a plan which he knows will be accepted for sure and will maximize his gold. What is his plan?

### How Strong is an Egg?

You have two identical eggs. Standing in front of a 100 floor building, you wonder what is the maximum number of floors from which the egg can be dropped without breaking it. What is the minimum number of tries needed to find out the solution?

### What’s Your Eye Color?

On a certain island there are people with assorted eye colors. There are 100 people with blue eyes and 100 people with brown eyes. Since there are no mirrors on this island, no person knows the color of their own eyes. The people on the island are not allowed to talk or communicate with each other in any way. They are also NOT aware of the number of blue or brown eyed people on the island. For all they know, they could have red eyes too. But they are allowed to observe other people and keep count of the number of people with a certain eye color. There is a rule that the people on the island have to follow – any person who is sure of their eye color has to leave the island immediately.

One day, an outsider comes to the island and announces to the people that he sees someone with blue eyes. What do you think happens?

One day, an outsider comes to the island and announces to the people that he sees someone with blue eyes. What do you think happens?

### Bulb Or No Bulb?

There are 100 bulbs arranged in a row. Each bulb has its own switch and is currently turned off. In the first round, you turn every switch on. In the second round, you flip the switch of every second bulb (i.e. bulb 2, 4, 6, 8 and so on). In the third round, you flip the switch of every third bulb and so on. What is the state of bulb 9 after 100 rounds? Also, how many bulbs are on after 100 rounds?

### 6 Pirates Fight for 1 Gold Coin

Six pirates discover a chest containing 1 gold coin. They decide to sit down and devise a distribution strategy. The pirates are ranked based on their experience (Pirate 1 to Pirate 6, where Pirate 6 is the most experienced). The most experienced pirate gets to propose a plan and then all the pirates vote on it. If at least half of the pirates agree on the plan, the gold is split according to the proposal. If not, the most experienced pirate is thrown off the ship and this process continues with the remaining pirates until a proposal is accepted. The first priority of the pirates is to stay alive and second to maximize the gold they get. Pirate 6 devises a plan which he knows will keep him alive. What is his plan?

### 9 Minutes

You are given two hourglasses. One measures 4 minutes and one measures 7 minutes. How would you measure exactly 9 minutes?

### Three Switches

You are standing outside a room next to three switches, all of which are off. Each switch operates a different light bulb in the room. The room door is closed, so you cannot see which switch operates which bulb. You are only allowed to go into the room once. Determine which switch operates which bulb.

### Farmer’s Dilemma

A farmer bought a goat, a wolf and a cabbage from the market. On his way home, he has to cross a river. He has a small boat which only allows him to take one thing with him at a time. The farmer cannot leave the cabbage and the goat together (the goat would eat the cabbage) nor can he leave the goat and the wolf together (the wolf would eat the goat). How does he cross the river without losing any of the things he bought?

### Tunnel Trouble

A man needs to go through a train tunnel to reach the other side. He starts running through the tunnel in an effort to reach his destination as soon as possible. When he is 1/4th of the way through the tunnel, he hears the train whistle behind him. Assuming the tunnel is not big enough for him and the train, he has to get out of the tunnel in order to survive. We know that the following conditions are true.

1. If he runs back, he will make it out of the tunnel by a whisker.

2. If he continues running forward, he will still make it out through the other end by a whisker.

What is the speed of the train compared to that of the man?

1. If he runs back, he will make it out of the tunnel by a whisker.

2. If he continues running forward, he will still make it out through the other end by a whisker.

What is the speed of the train compared to that of the man?

### Globe Walker

How many points are there on the globe where, by walking one mile south, then one mile east and then one mile north, you would reach the place where you started?

### Trains and Birds

A train leaves City X for City Y at 15 mph. At the very same time, a train leaves City Y for City X at 20 mph on the same track. At the same moment, a bird leaves the City X train station and flies towards the City Y train station at 25 mph. When the bird reaches the train from City Y, it immediately reverses direction. It then continues to fly at the same speed towards the train from City X, when it reverses its direction again, and so forth. The bird continues to do this until the trains collide. How far would the bird have traveled in the meantime?

### Burning Sticks

You have two sticks and matchbox. Each stick takes exactly an hour to burn from one end to the other. The sticks are not identical and do not burn at a constant rate. As a result, two equal lengths of the stick would not necessarily burn in the same amount of time. How would you measure exactly 45 minutes by burning these sticks?

### The Fox and The Duck

A duck that is being chased by a fox saves itself by sitting at the center of circular pond of radius r. The duck can fly from land but cannot fly from the water. Furthermore, the fox cannot swim. The fox is four times faster than the duck. Assuming that the duck and fox are perfectly smart, is it possible for the duck to ever reach the edge of the pond and fly away to its escape from the ground?

### Chasing Dogs

There are four dogs each at the corner of a unit square. Each of the dogs starts chasing the dog in the clockwise direction. They all run at the same speed and continuously change their direction accordingly so that they are always heading straight towards the other dog. How long does it take for the dogs to catch each other and where?

### Boxes of Money

You are given b boxes and n dollar bills. The money has to be sealed in the b boxes in a way such that without thereafter opening a box, you can give someone a requested whole amount of dollars from 0 to n. How should b be related to n for this to happen?

### One train leaves Los Angeles

One train leaves Los Angeles at 15 MPH heading for New York . Another train leaves from New York at 20mph heading for Los Angeles on the same track. If a bird, flying at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth between the two trains until they collide, how far will the bird have traveled?

### Sheriff in a town that caught three outlaws

There was a sheriff in a town that caught three outlaws. He said he was going to give them all a chance to go free. All they had to do is figure out what color hat they were wearing. The sheriff had 5 hats, 3 black and 2 white. Each outlaw can see the color of the other outlaw’s hats, but cannot see his own. The first outlaw guessed and was wrong so he was put in jail. The second outlaw also guessed and was also put in jail. Finally the third blind outlaw guessed and he guessed correctly. How did he know?

### Fuse ropes

You are given two 60 minute long fuse ropes (i.e. the kind that you would find on the end of a bomb) and a lighter. The fuses do not necessarily burn at a fixed rate. For example, given an 8 foot rope, it may take 5 minutes for the first 4 feet of the fuse to burn, while the last 4 feet could take 55 minutes to burn (a much slower rate) (5+55=60 minutes). Using these two fuses and the lighter, how can you determine 45 minutes? HINT: You can use the lighter any number of times

### Three wise men in a room

There are three wise men in a room: A, B and C. You decide to give them a challenge. Suspecting that the thing they care about most is money, you give them $100 and tell them they are to divide this money observing the following rule: they are to discuss offers and counter-offers from each other and then take a vote. The majority vote wins. Sounds easy enough... now the question is, assuming each person is motivated to take the largest amount possible, what will the outcome be?

### 5 houses in 5 different colors

This puzzle was apparently written by Einstein in the last century.

He said that 98% of the people in the world cannot solve the quiz. See if you can...

Facts:

1: There are 5 houses in 5 different colors

2: In each house lives a person with a different nationality.

3: These 5 owners drink a certain beverage, smoke a certain brand of cigar and keep a certain pet.

4: No owner has the same pet, smoke the same brand of cigar or drink the same drink.

Hints:

1: The British lives in a red house.

2: The Swede keeps dogs as pets

3: The Dane drinks tea

4: The green house is on the left of the white house (it also means they are next door to each other)

5: The green house owner drinks coffee

6: The person who smokes Pall Mall rears birds

7: The owner of the yellow house smokes Dunhill

8: The man living in the house right in the center drinks milk

9: The Norwegian lives in the first house

10: The man who smokes Blend lives next to the one who keeps cats

11: The man who keeps horses lives next to the man who smokes Dunhill

12: The owner who smokes Blue Master drinks beer

13: The German smokes Prince

14: The Norwegian lives next to the blue house

15: The man who smokes Blend has a neighbor who drinks water.

The question is: who keeps the fish?

He said that 98% of the people in the world cannot solve the quiz. See if you can...

Facts:

1: There are 5 houses in 5 different colors

2: In each house lives a person with a different nationality.

3: These 5 owners drink a certain beverage, smoke a certain brand of cigar and keep a certain pet.

4: No owner has the same pet, smoke the same brand of cigar or drink the same drink.

Hints:

1: The British lives in a red house.

2: The Swede keeps dogs as pets

3: The Dane drinks tea

4: The green house is on the left of the white house (it also means they are next door to each other)

5: The green house owner drinks coffee

6: The person who smokes Pall Mall rears birds

7: The owner of the yellow house smokes Dunhill

8: The man living in the house right in the center drinks milk

9: The Norwegian lives in the first house

10: The man who smokes Blend lives next to the one who keeps cats

11: The man who keeps horses lives next to the man who smokes Dunhill

12: The owner who smokes Blue Master drinks beer

13: The German smokes Prince

14: The Norwegian lives next to the blue house

15: The man who smokes Blend has a neighbor who drinks water.

The question is: who keeps the fish?

### 5 Jars of pills

You have 5 jars of pills. Each pill weighs 10 grams, except for contaminated pills contained in one jar, where each pill weighs 9 grams. Given a scale, how could you tell which jar had the contaminated pills in just one measurement?

### One gold bar

You have someone working for you for seven days and you have one gold bar to pay them. The gold bar is segmented into seven connected pieces. You must give them a piece of gold at the end of every day. If you are only allowed to make two breaks in the gold bar, how do you pay your worker?

### Cross a bridge

There are four people who need to cross a bridge at night. The bridge is only wide enough for two people to cross at once. There is only one flashlight for the entire group. When two people cross, they must cross at the slower member's speed. All four people must cross the bridge in 17 minutes, since the bridge will collapse in exactly that amount of time. Here are the times each member takes to cross the bridge:

Person A: 1 minute

Person B: 2 minutes

Person C: 5 minutes

Person D: 10 minutes

If Person A and C crossed the bridge initially, 5 minutes would elapse, because Person C takes 5 minutes to cross. Then Person A would have to come back to the other side of the bridge, taking another minute, or six minutes total. Now, if Person A and D crossed the bridge next, it would take them 10 minutes, totaling to 16 minutes. If A came back, it would take yet another minute, totally 17. The bridge would collapse with A and B on the wrong side. How can all four people get across the bridge within 17 minutes? Note: there is no trick-answer to this problem.

Person A: 1 minute

Person B: 2 minutes

Person C: 5 minutes

Person D: 10 minutes

If Person A and C crossed the bridge initially, 5 minutes would elapse, because Person C takes 5 minutes to cross. Then Person A would have to come back to the other side of the bridge, taking another minute, or six minutes total. Now, if Person A and D crossed the bridge next, it would take them 10 minutes, totaling to 16 minutes. If A came back, it would take yet another minute, totally 17. The bridge would collapse with A and B on the wrong side. How can all four people get across the bridge within 17 minutes? Note: there is no trick-answer to this problem.

### Rectangular cake

If given a rectangular cake with a rectangular piece removed (any size or orientation), how would you cut the remainder of the cake into two equal halves with one straight cut of a knife?

### Life or Death? The Emperor's Proposition

You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles and 2 empty bowls. He then says, "Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove ONE marble. If the marble is WHITE you will live, but if the marble is BLACK... you will die."

How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble?

How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble?

### Birthday Line

At a movie theater, the manager announces that they will give a free ticket to the first person in line whose birthday is the same as someone who has already bought a ticket. You have the option of getting in line at any time. Assuming that you don't know anyone else's birthday, that birthdays are distributed randomly throughout the year, etc., what position in line gives you the greatest chance of being the first duplicate birthday?

### Russian Roulette

You are in a game of Russian Roulette with a revolver that has 3 bullets placed in three consecutive chambers. The cylinder of the gun will be spun once at the beginning of the game. Then, the gun will be passed between two players until it fires. Would you prefer to go first or second?

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