Puzzles
Suppose you are in a hallway lined with 100 closed lockers. You begin by opening all 100 lockers. Next, you close every second locker. Then you go to every third locker and close it if it is open or open it if it is closed (call this toggling the locker). Continue toggling every nth locker on pass number n. After your hundredth pass of the hallway, in which you toggle only locker number 100, how many lockers are open?
(The correct answer is 10)
Bear Hunting
"A man is out hunting. He walks one mile south. He makes a ninety degree turn to his left. He walks another mile. He makes another ninety degree turn to his left and walks another mile. He is now back where he first started. He shoots a bear. What color is the bear?"
Spinning Wheel
"A wheel is painted half black and half white. You can place two stationary sensors anywhere on the surface of the wheel. The sensors tell you what color they see. How can you tell which way the wheel is spinning? And how long does it take before you know?"
A Pirate as Emissary
"There are two kings, each on an island. Each king has one valuable diamond, one box, one lock, and one key. The king on the first island has a daughter (so we'll call him the Daughter King). The king on the second island has a son (so we'll call him the Son King).
"The only way between the islands is a pirate ship. The pirate is open to doing a bit of commerce, but he's a pirate. If he can get the diamond and keep it, he will. The kings, on the other hand, are honest, which is to say that they don't steal and they keep their word.
"The kings are trying to arrange a marriage between their respective offspring. The diamond is what proves how great a king is. The Son King has demanded to see the diamond belonging to the Daughter King. The Daughter King is willing to show it to him. How can he show off his diamond (and get it back) without any possibility of its being stolen? "
You have 2 candles. Every candle lights for 60 minutes. You have to find the way to measure 45 minutes.
A snail wants to creep on to the top of the tree 5 m high.During the day it can creep up 3m but during the night it creeps down 2m. How many days does it need to reach the top?
There are 3 switches in one room that control 3 electrical lamps located in the other room.You are allowed to spend 5 minutes in the room with switches,change their position as you want.Then you should go to the room with lamps and tell exactly what switch controls every lamp.You can't return to the room with switches.
There is a pot full of water. How to pour out half of it without using a meter?
9 coins,one of them is fake. Use a balance to weigh them not more than 3 times and find the fake.A fake coin is not necessarily lighter.
Connect 9 dots with 4 lines . Don't cross the same dot twice.
A point is chosen at random from within a circular region.What is the probability that the point is closer to the center of the region than it is to the boundary of the region.
Why are manhole covers round ?
Parachutist is landing the island in the darkness. The island is of unknown shape. There must be a fenced lot at the island. The parachutist needs to find out if he is within the fenced lot or outside.
If you ask electronics engineer " To be or not to be ?" , his answer will be "One!" How come?
A band is going in the street with a constant speed.Someone in the last raw has a dog.The dog runs ahead, reaches the front line of the band and gets back to it's owner. The dog's speed was also constant all the way and while it was running the band passed 50 feet. Find the length of the dog's path,if the distance between the front and the rear line of the band is 50 feet.
You are playing a game with your partner.The idea is to cover a round table with quaters. The one who puts the last coin - wins.Suggest a winning strategy.
There are 100 gold coins in 10 columns by 10 coins in each column. Every coin weights 1 lb. One column contains 10 fake coins.Each coin in it weights 0.9 lb. Take one measurement to find the column with fakes.
Two drivers are going to the next town which is 100 miles away. They depart at the same time, however the first driver stops for gas during the first 50 miles, the second driver stops during the second half. Each stop takes 10 minutes. They both drive with the same speed 60 mph during the first 50 miles and 65 mph during the second half. Who, do you think, arrives first?
A chess board has 64 squares.Two squares in the diagonal corners are masked out.Is it possible to cover the rest 62 squares with 31 dominos? (One domino covers two squares.) Explain the logic of your answer.
How to cut a plain circular cake for 8 people with just three straight cuts of knife?
There are four numbers: 1, 2, 5, 10 that you have to carry in a boat across a river. Every time you may not carry more than two numbers , and the time of traveling is associated with the largest of two numbers. One number has to be in the boat during the return journey, which also defines the time for this trip. What is the minimum total time to carry all numbers from one bank to another?
A man went down to the river with two jugs, one of three-liter capacity and one of five-liter capacity. Using just these , how did he bring back exactly four liters?
You drove to the next town with a speed of 60 miles/hour. On your way back the speed was 40 miles/hour. The distance is 120 miles. Calculate the average speed.
A man is running across a bridge.When he is 3/8 of the way accross, he heard a train coming behind him. If he keeps running he will reach the end of the bridge at the same time with the train. If he turns around and runs back, he will get to the beginning of the bridge at the same time with the train. The man runs at a speed of 5mph. What is the speed of the train?
We are going to play a paper-rock game (similar to paper-rock-scissors). If we both have "paper" - I pay you $3, if we both have "rock" - I pay you $1. If they don't match - you pay me $2. Suggest a winning strategy?
You are sitting in a boat in the middle of a lake. You pick up a rock from the boat and throw it into the lake. Did your action raise or lower the water level at the edge of the lake?
If you are in a dark room with a candle, a wood stove and a gas lamp. You only have one match, so what do you light first?
Would you rather a crocodile attack you or an alligator?
A customer at a 7-11 store selected four items to buy, and was told that the cost was $7.11. He was curious that the cost was the same as the store name, so he enquired as to how the figure was derived. The clerk said that he had simply multiplied the prices of the four individual items. The customer protested that the four prices should have been ADDED, not MULTIPLIED. The clerk said that that was OK with him, but, the result was still the same: exactly $7.11. What were the four prices?
A rich aristocrat decided that he would give every man $45 and every woman $60. Only one ninth of the men and only one twelfth of the women collected their dues. Can you tell me how much money the aristocrat spent if there were 3552 people in total?
The local river Trent is 4100 inches wide, which happens to be a fantastic number. There is a magnificent bridge which spans the river. During a recent survey of the area it was found that one seventh of the overall length of the bridge was on one side of the river and one eighth of the bridge was on the other side of the river. How long is the bridge which spans the river Trent?
After visiting my Great Aunt Anne, I travelled home in my old jalopy. The car was so old and battered, I was stuck in second gear. This meant that I could only travel along at a steady 30 miles per hour and managed a paltry 20 miles per gallon of fuel. At the start of the journey I had placed exactly 10 gallons of fuel into the tank. I knew though, that the fuel tank lost fuel at the rate of half a gallon per hour. As I arrived home, the car stopped because it had run out of fuel and I only just made it. How far was it from my Great Aunt's to my home?
A large fresh water reservoir has two types of drainage system. Small pipes and large pipes. 6 large pipes, on their own, can drain the reservoir in 12 hours. 6 small pipes, on their own, can drain the reservoir in 18 hours. How long will 6 large pipes and 6 small pipes take to drain the reservoir?
Add a single straight line to make this equation true - the equals sign remains untouched.
5 + 5 + 5 = 550
One family wants to get through a tunnel. Dad can make it in 1 minute, mama in 2 minutes, son in 4 and daughter in 5 minutes. Unfortunately, through the tight tunnel can go at once not more than two persons moving at the speed of the slower one.Can they all make it if they have a torch that lasts only 12 minutes and they are afraid of the dark?
A farmer is returning from market, where he bought a she-goat, a wolf and cabbage. On the way home he must cross a river. His boat is little, allowing to take on it only one of the three things. There can't stay together the she-goat and the cabbage (because the she-goat would eat it), neither the she-goat with the wolf (because she-goat would be bitten .How will the farmer get everything on the other side (without any harm)?
Suppose you are in a hallway lined with 100 closed lockers. You begin by opening all 100 lockers. Next, you close every second locker. Then you go to every third locker and close it if it is open or open it if it is closed (call this toggling the locker). Continue toggling every nth locker on pass number n. After your hundredth pass of the hallway, in which you toggle only locker number 100, how many lockers are open?
(The correct answer is 10)
Bear Hunting
"A man is out hunting. He walks one mile south. He makes a ninety degree turn to his left. He walks another mile. He makes another ninety degree turn to his left and walks another mile. He is now back where he first started. He shoots a bear. What color is the bear?"
Spinning Wheel
"A wheel is painted half black and half white. You can place two stationary sensors anywhere on the surface of the wheel. The sensors tell you what color they see. How can you tell which way the wheel is spinning? And how long does it take before you know?"
A Pirate as Emissary
"There are two kings, each on an island. Each king has one valuable diamond, one box, one lock, and one key. The king on the first island has a daughter (so we'll call him the Daughter King). The king on the second island has a son (so we'll call him the Son King).
"The only way between the islands is a pirate ship. The pirate is open to doing a bit of commerce, but he's a pirate. If he can get the diamond and keep it, he will. The kings, on the other hand, are honest, which is to say that they don't steal and they keep their word.
"The kings are trying to arrange a marriage between their respective offspring. The diamond is what proves how great a king is. The Son King has demanded to see the diamond belonging to the Daughter King. The Daughter King is willing to show it to him. How can he show off his diamond (and get it back) without any possibility of its being stolen? "
You have 2 candles. Every candle lights for 60 minutes. You have to find the way to measure 45 minutes.
A snail wants to creep on to the top of the tree 5 m high.During the day it can creep up 3m but during the night it creeps down 2m. How many days does it need to reach the top?
There are 3 switches in one room that control 3 electrical lamps located in the other room.You are allowed to spend 5 minutes in the room with switches,change their position as you want.Then you should go to the room with lamps and tell exactly what switch controls every lamp.You can't return to the room with switches.
There is a pot full of water. How to pour out half of it without using a meter?
9 coins,one of them is fake. Use a balance to weigh them not more than 3 times and find the fake.A fake coin is not necessarily lighter.
Connect 9 dots with 4 lines . Don't cross the same dot twice.
A point is chosen at random from within a circular region.What is the probability that the point is closer to the center of the region than it is to the boundary of the region.
Why are manhole covers round ?
Parachutist is landing the island in the darkness. The island is of unknown shape. There must be a fenced lot at the island. The parachutist needs to find out if he is within the fenced lot or outside.
If you ask electronics engineer " To be or not to be ?" , his answer will be "One!" How come?
A band is going in the street with a constant speed.Someone in the last raw has a dog.The dog runs ahead, reaches the front line of the band and gets back to it's owner. The dog's speed was also constant all the way and while it was running the band passed 50 feet. Find the length of the dog's path,if the distance between the front and the rear line of the band is 50 feet.
You are playing a game with your partner.The idea is to cover a round table with quaters. The one who puts the last coin - wins.Suggest a winning strategy.
There are 100 gold coins in 10 columns by 10 coins in each column. Every coin weights 1 lb. One column contains 10 fake coins.Each coin in it weights 0.9 lb. Take one measurement to find the column with fakes.
Two drivers are going to the next town which is 100 miles away. They depart at the same time, however the first driver stops for gas during the first 50 miles, the second driver stops during the second half. Each stop takes 10 minutes. They both drive with the same speed 60 mph during the first 50 miles and 65 mph during the second half. Who, do you think, arrives first?
A chess board has 64 squares.Two squares in the diagonal corners are masked out.Is it possible to cover the rest 62 squares with 31 dominos? (One domino covers two squares.) Explain the logic of your answer.
How to cut a plain circular cake for 8 people with just three straight cuts of knife?
There are four numbers: 1, 2, 5, 10 that you have to carry in a boat across a river. Every time you may not carry more than two numbers , and the time of traveling is associated with the largest of two numbers. One number has to be in the boat during the return journey, which also defines the time for this trip. What is the minimum total time to carry all numbers from one bank to another?
A man went down to the river with two jugs, one of three-liter capacity and one of five-liter capacity. Using just these , how did he bring back exactly four liters?
You drove to the next town with a speed of 60 miles/hour. On your way back the speed was 40 miles/hour. The distance is 120 miles. Calculate the average speed.
A man is running across a bridge.When he is 3/8 of the way accross, he heard a train coming behind him. If he keeps running he will reach the end of the bridge at the same time with the train. If he turns around and runs back, he will get to the beginning of the bridge at the same time with the train. The man runs at a speed of 5mph. What is the speed of the train?
We are going to play a paper-rock game (similar to paper-rock-scissors). If we both have "paper" - I pay you $3, if we both have "rock" - I pay you $1. If they don't match - you pay me $2. Suggest a winning strategy?
You are sitting in a boat in the middle of a lake. You pick up a rock from the boat and throw it into the lake. Did your action raise or lower the water level at the edge of the lake?
If you are in a dark room with a candle, a wood stove and a gas lamp. You only have one match, so what do you light first?
Would you rather a crocodile attack you or an alligator?
A customer at a 7-11 store selected four items to buy, and was told that the cost was $7.11. He was curious that the cost was the same as the store name, so he enquired as to how the figure was derived. The clerk said that he had simply multiplied the prices of the four individual items. The customer protested that the four prices should have been ADDED, not MULTIPLIED. The clerk said that that was OK with him, but, the result was still the same: exactly $7.11. What were the four prices?
A rich aristocrat decided that he would give every man $45 and every woman $60. Only one ninth of the men and only one twelfth of the women collected their dues. Can you tell me how much money the aristocrat spent if there were 3552 people in total?
The local river Trent is 4100 inches wide, which happens to be a fantastic number. There is a magnificent bridge which spans the river. During a recent survey of the area it was found that one seventh of the overall length of the bridge was on one side of the river and one eighth of the bridge was on the other side of the river. How long is the bridge which spans the river Trent?
After visiting my Great Aunt Anne, I travelled home in my old jalopy. The car was so old and battered, I was stuck in second gear. This meant that I could only travel along at a steady 30 miles per hour and managed a paltry 20 miles per gallon of fuel. At the start of the journey I had placed exactly 10 gallons of fuel into the tank. I knew though, that the fuel tank lost fuel at the rate of half a gallon per hour. As I arrived home, the car stopped because it had run out of fuel and I only just made it. How far was it from my Great Aunt's to my home?
A large fresh water reservoir has two types of drainage system. Small pipes and large pipes. 6 large pipes, on their own, can drain the reservoir in 12 hours. 6 small pipes, on their own, can drain the reservoir in 18 hours. How long will 6 large pipes and 6 small pipes take to drain the reservoir?
Add a single straight line to make this equation true - the equals sign remains untouched.
5 + 5 + 5 = 550
One family wants to get through a tunnel. Dad can make it in 1 minute, mama in 2 minutes, son in 4 and daughter in 5 minutes. Unfortunately, through the tight tunnel can go at once not more than two persons moving at the speed of the slower one.Can they all make it if they have a torch that lasts only 12 minutes and they are afraid of the dark?
A farmer is returning from market, where he bought a she-goat, a wolf and cabbage. On the way home he must cross a river. His boat is little, allowing to take on it only one of the three things. There can't stay together the she-goat and the cabbage (because the she-goat would eat it), neither the she-goat with the wolf (because she-goat would be bitten .How will the farmer get everything on the other side (without any harm)?
where are the answers...
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