Lets Think!!!!!!!!!!!!!!!!!!!!!!!!!!

2013-02-17T04:14:00.001-08:00

OFF-CENTER WHEEL

2011-08-14T03:08:00.000-07:00

Lolinsan looked at the piece of wood before him. It is a 10” diameter round, flat piece he wanted to use as a “wheel” in his art lesson homework. Alas! While drilling the center hole (1” diameter) , he sneezed, and the hole is way off-center (although, luckily, still within the “wheel” – the center of the hole is 3” away from the center of the wheel).

And then, revelation! Willy cuts the wheel into two parts, glued them again, and got a perfectly centered hole in the wheel. How did he do it?

Note: assume lolinsan has in his possession a magical cutter that cuts with zero width, and magic glue that can glue pieces with zero distance between them.

MATCH EQUATIONS

2011-08-14T03:06:00.001-07:00

In each of the following three configurations of matches, move a single match to form valid equations. The = and + are composed of two matches each.

\/|+|=\/
\/|+|=\/|
\/|+|=|||

HOTEL INFINITY

2011-08-14T03:03:00.000-07:00

So, an eccentric entrepreneur by the name of Alphonse Null has sent out a press release about his new, mind-blowing hotel: The Hotel Infinity. Null informs the world that this hotel has an infinite number of rooms (specifically, an infinity equal to the cardinality of the integers). A quick tour puts skeptics' claims to rest; as far as anyone can tell, this hotel has infinite rooms. The consequences are mind-boggling, and Null sets up a press conference to answer questions...

"So, Mr. Null, how will patrons get to their room, if their room number has, say, more digits than protons in the universe?"

"The elevators have an ingenious formula device instead of buttons... simply input the formula for your room number, with Ackermann numbers or somesuch... your room formula can be picked up at the front desk. There's not even any need to know what the formula means!"

"How do you produce the power and water for this hotel?"

"I have infinite generators and wells, of course. This IS an infinite hotel, you know! *chuckle*"

"What about costs? How much will it cost to stay here?"

"That's the beauty of it! Since there are as many positive even integers as there are integers, I can change the same price to only every other room and still make the same profit! I could charge only every millionth room... each guest has a one-in-a-million chance of not getting a free room, and I still get paid the same! I love the properties of infinite sets, especially when it comes to profit!"

"But, Mr. Null... I think you've made a severe mistake in your assumptions regarding profit..."

"Oh?"

The reporter then mentioned something which made Mr. Null's face turn white.

"Oh... oh goodness... THIS PRESS CONFERENCE IS OVER!" Then he ran out.

Assuming that everything Null said about the hotel is true: it really is infinite; it really is easy to get to your room; it really can generate infinite power for the guests; the cardinality of the set of multiples of a million, is the same as the cardinality of the integers...

So with what simple assumption did Mr. Null go wrong?

FRYING FOOD

2011-08-14T02:46:00.000-07:00

The boiling point of olive oil is higher than the melting point of tin. If Italian skillets are made of tinned copper, how can they be used to fry food in olive oil?

DOMINANT FIFTH

2011-08-14T02:44:00.000-07:00

"What's the Dominant Fifth?" asked Dr. Dingo, as his daughter Cicely came in from school.

Cicely blushed. "Just a secret society," she said. "I'm one of the vice-presidents."

"And you're meeting tonight; is that right?"

"How on earth did you know?" ask Cicely.

"You left this lying about. That's no way to keep secrets, my girl." He handed Cicely this paper:

Dominant Fifth

REASM NCNVE OTMLE SEHST TAOEI

"How did you manage to read it?" asked Cicely. "The code is known to only about eight of us."

"Change it," said Dingo. "Any fool can read that."

Where and When is the next meeting scheduled?

RIVER CROSSING

2011-08-13T23:12:00.000-07:00

Two people come to a river. There is a boat, however it can carry one person only. How can they each get to the other side of the river using the boat?

ENVELOPE GAMBLE

2011-08-13T07:52:00.000-07:00

I have a distribution over the Reals which you do not know. I choose two numbers from it, and write them inside envelopes. You are given one of the envelopes, and allowed to see the number inside it. Then, you are given the option to switch envelopes once. After you settle on an envelope, you win the amount inside your envelope, and you pay the amount inside the other envelope. Can you win money playing this game, with a strategy independent of my distribution?

PAST, PRESENT, FUTURE

2011-08-13T07:51:00.001-07:00

There are three omniscient gods sitting in a chamber: Past, Present and Future. They are all truthful, but with the following caveat: Present answers the question currently being asked, Past answers the last question asked in their chamber, and Future answers the next question which will be asked in their chamber. Despite their manipulation of which question to answer, each still answers immediately as if answering the question currently being asked.

Furthermore, the gods answer in a language in which "yes" and "no" are replaced by "da" and "ya", but you do not know which is which. You only know that their answers are consistent amongst themselves.

With three questions, determine which god is which.

POP QUIZ

2011-08-13T07:43:00.001-07:00

The professor for class Logic 315 says on Friday: "We're going to have a surprise quiz next week, but I'm not telling you what day... if you can figure out what day it will be on, I'll cancel the quiz."

The students get together and decide that the quiz can't be on Friday, as if the quiz doesn't happen by Thursday, it'll be obvious the quiz is on Friday. Similarly, the quiz can't be on Thursday, because we know it won't be on Friday, and if the quiz doesn't happen by Wednesday, it'll be obvious it's on Thursday (because it can't be on Friday). Same thing for Wednesday, Tuesday and Monday. So it can't be on ANY day, so there's no quiz next week!"

They tell the professor, who smiles and says, "Well, nice to see you're thinking about it."

On Tuesday, the professor gives the quiz, totally unexpected!

What's the flaw in the students' thinking?

Never ask a womens age :P

2011-07-17T03:27:00.000-07:00

In the pub of a quiet little village, the bartender and the local school teacher had the following conversation. The bartender said: "Pastor Petersen was visited by three women today. Can you work out how old they are, if you know that the product of their ages is 2450, and that together they are as old as you are?" After a deep consideration, the teacher said: "No, I can't." Then the bartender said: "Of course you can't, but if I tell you that the oldest woman is older than pastor Petersen, you should be able to work it out." The teacher did. Can you find out how old is pastor Petersen?

The flippant number

2011-07-17T03:24:00.000-07:00

A positive integer n is called “ﬂippant” if n does not end in 0 (when written in decimal
notation) and, moreover, n and the number obtained by reversing the digits of n are
both divisible by 7. How many ﬂippant integers are there between 10 and 1000

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Funbit

2011-07-17T03:16:00.001-07:00

It's always 1 to 6, it's always 15 to 20, it's always 5, but it's never 21, unless it's flying. What is this?

Click here for the answer

Lateral Thinking Puzzles

2011-07-16T05:02:00.000-07:00

1. One day Kerry celebrated her birthday. Two days later her older twin brother, Terry, celebrated his birthday. How come?

2. Deep in the forest was found the body of a man who was wearing only swimming trunks, snorkel and face mask. The nearest lake was 8 miles away and the sea was 100 miles away. How had he died?

3. A blind beggar had a brother who died. What relation was the blind beggar to the brother who died? (Brother is not the answer).

4. A man went to a party and drank some of the punch. He then left early. Everyone else at the party who drank the punch subsequently died of poisoning. Why did the man not die?

5. Several truck drivers at a roadside cafe started to play poker. The pot was large and the game was serious. Suddenly one of the men accused the dealer of cheating. The dealer drew a
knife and, in plain view of all the others, stabbed the man and killed him. The police were called and they interviewed everyone who had been present. But no man was arrested or charged with any offense. Why not?

6. A man was born in Boston, Massachusetts. Both his parents were born in Boston,
Massachusetts. He lived all his life in Boston but he was not a United States citizen. How come?

7. Why is it better to have round manhole covers than square ones?

8. John and David were brothers. John married Jane. David married Diana. The strange thing was, John and Diana shared the same wedding anniversary. David's wedding anniversary was one month before this date and Jane's was one month after it. None of them had ever been divorced or remarried.What was going on here?

9. A truck became wedged under a low bridge. It could not move forward or backward without severely damaging its roof. The truck driver was perplexed until the little girl standing nearby suggested an easy solution. What was it?

10. A man rode into town on Friday. He stayed for three nights and then left on Friday. How come?

11. A woman had two sons who were born on the same hour of the same day of the same year. But they were not twins. How could this be so?

12. When Archduke Ferdinand was shot, in 1914, his attendants could not undo his coat to stem his bleeding wound. Why not?

13. During WWII, why did German soldiers have to shoot the dogs they had carefully trained?

14. Anthony and Cleopatra are lying dead on the floor of a villa in Egypt. Nearby is broken glass. There is no mark on either of their bodies and they were not poisoned. How did they die?

15. A man lives on the tenth floor of a building. Every day, he takes the elevator to the first floor to go shopping. When he returns, he always takes the elevator to the seventh floor and walks the rest of the fight of stairs to his apartment in the tenth floor. Why does he do this?

16. One night during the Second World War, an allied bomber was on a mission over Germany. The plane was in perfect condition and everything on it worked properly. When it had reached its target, the pilot ordered the bomb doors open. They opened. He then ordered the bombs released. The were released. But the bombs did not fall from the plane. Why should this be so?

17. Five pieces of coal, a carrot, and a scarf are lying on the lawn. Nobody put them on the lawn, but there is a perfectly logical reason for them being there. What is it?

18. There were two Americans waiting at the entrance to the British Museum. One of them was the father of the other one's son. How could this be so?

19. Not far from Madrid, there is a large wooden barn. The barn is completely empty except for a dead man hanging from the central rafter. The rope around his neck is ten feet long and his feet are three feet from the ground. The nearest wall is 20 feet away. It is not possible to climb up the walls or along rafters, yet he hanged himself. How did he manage it?

20. What happened in the second half of the 20th century and will not happen again for another 4000 years?

21. Why did an old lady always answer the door wearing her hat and coat?

22. Many more children are involved as pedestrians in road accidents than might be expected from their numbers and road use. An expert on road accidents has put forward an ingenious theory to account for this. What do you think the theory might be?

23. Two drivers drove slowly and safely in the correct direction down a wide road before coming to a stop in front of a red stop light. A nearby police officer immediately arrested one of the drivers and let the other one driver off. The police officer had never seen or heard either driver before. Neither driver had a criminal record. They were both fully dressed and no one had been drinking. Both cars were in excellent roadworthy condition and had not been stolen. The arrested driver was charged and convicted. Of what?

24. A man locks his keys inside his car and is unable to get them out despite trying for an hour. A police officer comes along and offers to help. He discovers that the back door of the car is unlocked and he consequently recovers the keys. The man thanks him, but when the officer departs the man locks the back door, leaving the keys inside. Why?

25. A man wanted to construct an important building and he received tenders from a hundred builders, who each presented their qualifications and claimed to be the best builder around. How did he chose between them?

26. A very unlucky gambler had lost all his money . His friends organized a raffle, rigged so he would be sure to win. Knowing the ticket number he held, they filled a hat with tickets bearing the same number. The asked him to draw the winning number. "Well," they asked him, "who won?" "Not me, anyway," he replied sadly. What had happened?

27. A man is lying dead in a field. Next to him there is an unopened package. There is no other creature in the field. How did he die?

Some silly puzzles

2011-07-16T04:49:00.000-07:00

Puzzle 1. A man came into town on Friday, stayed three days, and then left on Friday. How did he do it?

Puzzle 2. There are two fathers and two sons on a boat. Each person caught one fish. None of the fish were thrown back. Three fish were caught. How is it possible?

Puzzle 3. A man pushed his car. He stopped when he reached a hotel at which point he knew he was bankrupt. Why?

Puzzle 4. What five-letter word becomes shorter when you add two letters to it?

Puzzle 5. A plane is going from the United States to Canada. It crashes right on the middle of the border. Where do you bury the survivors?

Puzzle 6. Captain Frank was out for a walk when it started to rain. He did not have an umbrella and he wasn't wearing a hat. His clothes were soaked, yet not a hair on his head got wet. How could this happen?

Puzzle 7. Not far from Madrid, there is a large wooden barn. The barn is completely empty except for a dead man hanging from the middle of the central rafter. The rope around his neck is ten feet long and his feet are three feet off the ground. The nearest wall is 20 feet away from the man. It is not possible to climb up the walls or along the rafters. The man hanged himself. How did he do it?

Puzzle 8. A man is lying dead in a field. Next to him there is an unopened package. There is no other creature in the field. How did he die?

Glass Half Full Or half Empty

2011-07-10T08:00:00.001-07:00

You are in an empty room and you have a transparent glass of water. The glass is a right cylinder, and it looks like it's half full, but you're not sure. How can you accurately figure out whether the glass is half full, more than half full, or less than half full? You have no rulers or writing utensils.

MONTY HALL SHOW

2011-07-10T07:58:00.001-07:00

You are a contestant on the Monty Hall game show. Three closed doors are shown before you. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does.

The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors.

After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch?

Hint: Like many other problems on this site, the first answer that comes to mind tends to be wrong. Try enumerating the possible outcomes in a tree-like structure, recording the probabilities of each event along the way.

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CHESSBOARD SQUARE AND RECTANGLE COUNT

2011-07-10T07:57:00.001-07:00

How many squares are on a chessboard (8 x 8)?

How many rectangles are on a chessboard?

8-WAY CAKE SLICE

2011-07-10T07:56:00.001-07:00

You have a round birthday cake. With three straight slices of a knife, divide the cake into 8 equal pieces. I know of two different solutions.

CLIMBING SNAIL

2011-07-10T07:55:00.001-07:00

A snail is at the bottom of a well that is 20 meters in depth. Every day the snail climbs 5 meters upwards, but at night it slides 4 meters back downwards. How many days must elapse till the snail reaches the top of the well?

APPLES AND ORANGES

2011-07-10T07:54:00.001-07:00

There are three closed and opaque cardboard boxes. One is labeled "APPLES", another is labeled "ORANGES", and the last is labeled "APPLES AND ORANGES". You know that the labels are currently misarranged, such that no box is correctly labeled. You would like to correctly rearrange these labels. To accomplish this, you may draw only one fruit from one of the boxes. Which box do you choose, and how do you then proceed to rearrange the labels?

COIN MACHINE WEIGHING

2011-07-10T07:50:00.000-07:00

you have 20 coin machines, each of which produce the same kind of coin. you know how much a coin is supposed to weigh. one of the machines is defective, in that every coin it produces weighs 1 ounce less than it is supposed to. you also have an electronic weighing machine. how can you determine which of the 20 machines is defective with only one weighing? (by one use, we mean you put a bunch of stuff on the machine and read a number, and that's it -- you not allowed to accumulate weight onto the machine and watch the numbers ascend, because that's just like multiple weighings). you are allowed to crank out as many coins from each machine as you like.

TWO COIN FLIPS

2011-07-10T07:48:00.001-07:00

i flip a penny and a dime and hide the result from you. "at least one of the coins came up heads", i announce. what is the chance that both coins came up heads?

Hint: Think again; conditional probability is often very nonintuitive. Write out a table of possibilities.

LOLINSAN AND THE BURNING ISLAND OF DOOM

2011-07-10T07:46:00.000-07:00

lolinsan(just a name) is hanging out on a heavily forested island that's really narrow: it's a narrow strip of land that's ten miles long. let's label one end of the strip A, and the other end B. a fire has started at A, and the fire is moving toward B at the rate of 1 mph. at the same time, there's a 2 mph wind blowing in the direction from A toward B. what can lolinsan do to save himself from burning to death?! assume that lolinsan can't swim and there are no boats, jetcopters, teleportation devices, etc.. (if he does nothing, lolinsan will be toasted after at most 10 hours, since 10 miles / 1 mph = 10 hours)

NONHOMOGENEOUS ROPE BURNING

2011-07-10T07:29:00.001-07:00

you have two ropes, each of which takes one hour to burn completely. both of these ropes are nonhomogeneous in thickness, meaning that some parts of the ropes are chunkier than other parts of the rope. using these nonhomogeneous ropes and a lighter, time 45 minutes.

Note: Some clarification on what is meant by nonhomogeneous. For instance, maybe a particular section of rope that is 1/8 of the total length is really chunky, and takes 50 minutes to burn off. then it would take 10 minutes to burn off the remaning 7/8, since we know that the whole rope takes an hour to burn off. that's just an example; we don't know any such ratios beforehand. The point is, if you look at one of your ropes and cut it into pieces, you have no clue how long any individual piece will take to burn off.