Sunday, August 14, 2011

OFF-CENTER WHEEL

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

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.

  1. \/|+|=\/
  2. \/|+|=\/|
  3. \/|+|=|||

HOTEL INFINITY

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

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

"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?

Saturday, August 13, 2011

RIVER CROSSING

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

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

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

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?

Sunday, July 17, 2011

Never ask a womens age :P

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

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

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

Saturday, July 16, 2011

Lateral Thinking Puzzles

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

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?

Sunday, July 10, 2011

Glass Half Full Or half Empty

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

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

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

How many rectangles are on a chessboard?

8-WAY CAKE SLICE

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

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

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

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

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

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

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.

HUMMINGBIRD

One train leaves Los Angeles at 15mph heading for New York. Another train leaves from New York at 20mph heading for Los Angeles on the same track. The distance between LA and NY is about 5000 miles. 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?

Saturday, July 9, 2011

Who am I? (11- 20)

11) The more you have of it, the less you see. What is it?

12) What has a head, a tail, is brown, and has no legs?

13) What English word has three consecutive double letters?

14) What's black when you get it, red when you use it, and white when you're all through with it?

15) You throw away the outside and cook the inside. Then you eat the outside and throw away the inside. What did you eat?

16) I am always hungry,
I must always be fed,
The finger I touch,
Will soon turn red

17) Ripped from my mother's womb,
Beaten and burned,
I become a blood thirsty killer.
What am I?

18) I know a word of letters three. Add two, and fewer there will be

19) I give you a group of three. One is sitting down, and will never get up. The second eats as much as is given to him, yet is always hungry. The third goes away and never returns.

20) I have four legs but no tail. Usually I am heard only at night. What am I?

21) Half-way up the hill, I see thee at last, lying beneath me with thy sounds and sights -- A city in the twilight, dim and vast, with smoking roofs, soft bells, and gleaming lights

22) When young, I am sweet in the sun.
When middle-aged, I make you gay.
When old, I am valued more than ever.

23) All about, but cannot be seen,
Can be captured, cannot be held,
No throat, but can be heard.

24) If you break me
I do not stop working,
If you touch me
I may be snared,
If you lose me
Nothing will matter.

25) Until I am measured
I am not known,
Yet how you miss me
When I have flown.

26) I drive men mad
For love of me,
Easily beaten,
Never free.

27) When set loose
I fly away,
Never so cursed
As when I go astray

28) Lighter than what
I am made of,
More of me is hidden
Than is seen

29) Each morning I appear
To lie at your feet,
All day I will follow
No matter how fast you run,
Yet I nearly perish
In the midday sun.

30) My life can be measured in hours,
I serve by being devoured.
Thin, I am quick
Fat, I am slow
Wind is my foe.

31) I am seen in the water
If seen in the sky,
I am in the rainbow,
A jay's feather,
And lapis lazuli.

32) Glittering points
That downward thrust,
Sparkling spears
That never rust.

33) You heard me before,
Yet you hear me again,
Then I die,
'Till you call me again.

34) Three lives have I.
Gentle enough to soothe the skin,
Light enough to caress the sky,
Hard enough to crack rocks.

35) At the sound of me, men may dream
Or stamp their feet
At the sound of me, women may laugh
Or sometimes weep

36) What does man love more than life
Fear more than death or mortal strife
What the poor have, the rich require,
and what contented men desire,
What the miser spends and the spendthrift saves
And all men carry to their graves?

37) I build up castles.
I tear down mountains.
I make some men blind,
I help others to see.
What am I?

38) Two in a corner,
1 in a room,
0 in a house, but 1 in a shelter. What am I?

39) Five hundred begins it, five hundred ends it,
Five in the middle is seen;
First of all figures, the first of all letters,
Take up their stations between.
Join all together, and then you will bring
Before you the name of an eminent king.

40) It cannot be seen, it weighs nothing, but when put into a barrel, it makes it lighter. What is it?

41) How far will a blind dog walk into a forest?

42) What happens when you throw a yellow rock into a purple stream?

43) What starts with a T, ends with a T, and has T in it?

44) As I went over London Bridge
I met my sister Jenny
I broke her neck and drank her blood
And left her standing empty

45) Whoever makes it, tells it not.
Whoever takes it, knows it not.
Whoever knows it, wants it not

46) I am, in truth, a yellow fork
From tables in the sky
By inadvertent fingers dropped
The awful cutlery.
Of mansions never quite disclosed
And never quite concealed
The apparatus of the dark
To ignorance revealed.

47) You saw me where I never was and where I could not be. And yet within that very place, my face you often see. What am I?

48) I turn polar bears white
and I will make you cry.
I make guys have to pee
and girls comb their hair.
I make celebrities look stupid
and normal people look like celebrities.
I turn pancakes brown
and make your champagne bubble.
If you squeeze me, I'll pop.
If you look at me, you'll pop.
Can you guess the riddle?

49) Say my name and I disappear. What am I?

50) What is it that after you take away the whole, some still remains?

51) A box without hinges, lock or key, yet golden treasure lies within. What is it?

52) Forward I'm heavy, but backwards I'm not. What am I?

53) Why doesn't a mountain covered with snow catch cold?

54) I can be long, or I can be short.
I can be grown, and I can be bought.
I can be painted, or left bare.
I can be round, or square.
What am I?

55) One by one we fall from heaven
down into the depths of past
And our world is ever upturned
so that yet some time we'll last

56) I drift forever with the current
down these long canals they've made
Tame, yet wild, I run elusive
Multitasking to your aid.
Before I came, the world was darker
Colder, sometimes, rougher, true
But though I might make living easy,
I'm good at killing people too.

57) Reaching stiffly for the sky,
I bare my fingers when it's cold
In warmth I wear an emerald glove
And in between I dress in gold

58) Kings and queens may cling to power
and the jester's got his call
But, as you may all discover,
the common one outranks them all

59) Every dawn begins with me
At dusk I'll be the first you see
And daybreak couldn't come without
What midday centers all about
Daises grow from me, I'm told
And when I come, I end all cold
But in the sun I won't be found
Yet still, each day I'll be around

60) Kings and lords and christians raised them
Since they stand for higher powers
Yet few of them would stand, I'm certain,
if women ruled this world of ours


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Friday, July 1, 2011

TRUTHS, FALSEHOOD, RANDOMNESS

Of three men, one man always tells the truth, one always tells lies, and one answers yes or no randomly. Each man knows which man is who. You may ask three yes/no question to determine who is who. If you ask the same question to more than one person you must count it as question used for each person whom you ask. What three questions should you ask?

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MOUSE EATING CHEESE CUBES

A cubic piece of cheese has been subdivided into 27 subcubes (so that it looks like a Rubik's Cube). A mouse starts to eat a corner subcube. After eating any given subcube it goes on to another adjacent subcube. Is it possible for the mouse to eat all 27 subcubes and finish with the center cube?

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BUTTON TRAP ROOM

You are trapped in a small phone booth shaped room. In the middle of each side of the room there is a hole. In each hole there is a push button that can be in either an off or on setting. You can't see in the holes but you can reach your hands in them and push the buttons. You can't tell by feel whether they are in the on or off position. You may stick your hands in any two holes at the same time and push neither, either, or both of the buttons as you please. Nothing will happen until you remove both hands from the holes. You succeed if you get all the buttons into the same position, after which time you will immediately be released from the room. Unless you escape, after removing your hands the room will spin around, disorienting you so you can't tell which side is which. How can you escape?

Now generalize. You are in a room with N sides, each side having a hole with a push button. What is the minimum number of hands you need to escape the trap room?

Note: Regarding the original setup with N = 4, the fewest possible turns that I know of is seven

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ENVELOPE GAMBLE I

There are two envelopes in front of you each with a non-zero sum of money. You are informed one has twice as much money as the other. You are then allowed to select either envelope and keep the money inside. After you select one and before opening it you are given the option to change your mind and switch to the other one? You think to yourself that if your envelope has x dollars there is a 50% chance the other one has x/2 dollars and a 50% chance it has 2x dollars. The expected return, you compute, is .5[.5x + 2x]=1.25x which seems like a favorable gamble. Do you switch and why? Assume you are neither risk averse nor risk prone, in other words you will take any good gamble and avoid any bad one.


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CARD GAME

Alice ---- "Here's the deal. You give me $10. Then I will deal four cards (from a regular 52 card deck), chosen randomly, face down. You get to look at #1 first and decide whether to keep it. If not, look at #2 and decide whether to keep that one. If not look at #3, and decide. If you don't take that, then #4 is your choice. If your chosen value is n, I will pay you $n. Then we can reshuffle the entire deck, you give me another $10, and we can play again, and again, and again."



Bob ------ "Hmmm....I need a good strategy to beat you at this game, but I think I can do it."



Help Bob out with a strategy that will win. Note that the cards all have face value with the following exceptions: Ace=1, Jack = 11, Queen = 12, and King = 13.


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HOTEL KEY CARD

A certain hotel room lock is opened by scanning a key card. In theory, one enters the room by inserting and removing the key card once. In practice, however, the key card is ambiguously labeled, so that either of two orientations might be the correct orientation of the card. In theory, of course, one could just try one orientation, and if it didn't work try the other. In practice, however, the card reader sometimes fails, so that after trying each orientation once, one may still not have gained access to the room.

A few more details:

(a) Either of the two orientations is equally likely to be cor- rect.

(b) The success rate of a correctly oriented card is p with 0 < p < 1.

(c) Failure on either side of the card is indistinguishable, so it does not give any information about whether the orientation of the card was correct.

(d) An attempted scan takes 1 second to succeed or fail; reversing the orientation also takes 1 second.

The last property means that in 3 seconds one could try one orientation 3 times or each orientation once (using the middle second to flip it over). In either case, of course, one might still be standing in the hall and need to decide what to do next.

So what attempt strategy would you use to enter the room? Why?

Feel free to consider fixed values of p (p = .5 or p = .9, for example) as special cases. What if p is fixed but unknown?

UPSIDE-DOWN LCD DISPLAY

In an LCD display some numbers, when viewed upside-down, are images of other numbers. For example, 1995 becomes 5661. The fifth number that can be read upside down is 8, and the 15th is 21, which is 12 when viewed upside-down. What is the millionth number that is meaningful upside-down?

MEAN, MEDIAN, NEITHER

Alice i was driving on a highway recently for one hour at a constant and very special speed.
Bob what was so special about it?
Alice the number of cars i passed was the same as the number of cars that passed me!
Bob your speed must have been the mean of the speeds of the cars on the road.
Alice or was it the median?
Bob these two are often confused. maybe it's neither? we'll have to think about this.

Was Alice's speed the mean, median, or neither?

Note: Assume that any car on the road drives at a constant nonzero speed of s miles per hour, where s is a positive inte- ger. And suppose that for each s, the cars driving at speed s are spaced uniformly, with d(s) cars per mile, d(s) being an integer. And because each mile looks the same as any other by the uniformity hypothesis, we can take mean and median to refer to the set of cars in a fixed one-mile segment, the half-open interval [M, M+1), at some instant.

7 BOOLEAN QUESTIONS

I am thinking of an integer n with 0 <= n <= 15. To figure out what number I'm thinking of, you can ask me 7 yes-or-no questions -- questions that can only be answered with either "yes" or "no". The questions must be independent of each other, their answers, and the order in which they are answered. (So you can't ask a question like, "if the answer to the previous question was "yes", then is n larger than 10, otherwise is n even?") When you ask me your seven questions, I am allowed to LIE about at most one of the answers. What seven questions can you ask to determine n?

MONOTONIC SUBSEQUENCE

Consider a finite sequence of distinct integers. A subsequence is a sequence formed by deleting some items from the original sequence without disturbing their relative ordering. A subsequence is called monotone if it is either increasing (each term is larger than the one before it) or decreasing (each term is smaller than the one before it). For example, if the sequence is 4, 6, 3, 5, 7, 1, 2, 9, 8, 10, then 4, 6, 8, 10 is a monotone (increasing) subsequence of length 4 and 6, 5, 2 is a monotone (decreasing) subsequence of length 3.

a) Find a sequence of 9 distinct integers that has no monotone subsequence of length 4.

b) Show that every such sequence of length 10 has a monotone subsequence of length 4.

c) Generalize. How long must the sequence be to guarantee a monotone subsequence of length n?

MESSAGE RECONSTRUCTION

alice sends different partial messages to a bunch of different receivers. by partial, we mean that one message by itself doesn't convey any meaningful information. let us denote the set of receivers as R. the messages are designed such that if any n receivers get together, they can somehow pool their partial messages together to get a meaningful message -- alice's intended message. however, if any n-1 or less receivers get together, they can't reconstruct anything meaningful whatsoever. n < |R|. what kind of messages are being sent by alice, and what mathematical function do the receivers apply on their pooled partial data to determine the intended message?

PEOPLE COMBINATIONS ROOM

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?

ZENO'S PARADOX

The Tortoise challenged the great warrior Achilles to a 100 meter foot race, claiming that he would win as long as Achilles granted him a little headstart. Achilles laughed, for he was a mighty warrior swift of foot, whereas the Tortoise was heavy and slow.

"How long of a head start do you need?" asked Achilles, smiling.
"Ten meters," said the Tortoise.
Achilles laughs. "OK, you will most definitely lose, but we can race if you really want."
"Actually, I will most definitely win, and I can prove it to you with a simple argument," said the Tortoise.
"Go on then," Achilles replied, with less confidence than he felt before. He knew he was the superior athlete, but he also knew the Tortoise had the sharper wits, and he had lost many a bewildering argument with him before this.
"Suppose," began the Tortoise, "that you give me a 10-meter head start. Would you say that you could cover that 10 meters between us very quickly?"
"Very quickly," Achilles affirmed.
"And in that time, how far should I have gone, do you think?"
"Perhaps a meter - no more," said Achilles after a moment's thought.
"Very well," replied the Tortoise, "so now there is a meter between us. And you would catch up that distance very quickly?"
"Very quickly indeed!"
"And yet, in that time I shall have gone a little way farther, so that now you must catch that distance up, yes?"
"Ye-es," said Achilles slowly.
"And while you are doing so, I shall have gone a little way farther, so that you must then catch up the new distance," the Tortoise continued smoothly.
Achilles said nothing.
"And so you see, in each moment you must be catching up the distance between us, and yet I - at the same time - will be adding a new distance, however small, for you to catch up again."
"Indeed, it must be so," said Achilles wearily.
"And so you can never catch up," the Tortoise concluded sympathetically.
"You are right, as always," said Achilles sadly - and conceded the race.

Was it really impossible for Achilles to win the race? Explain.

Thursday, June 30, 2011

PALINDROME DATES

"October 2, 2001" in MMDDYYYY format is a palindrome (a string that reads the same forwards as it does backwards). Pretty cool, check it out: 10/02/2001 --> 10022001. When was the last date before October 2, 2001 that is also a palindrome?

tell as many palindrome dates as possilble

DIFFERENTIATION DISASTER

We know that the derivative of x2 with respect to x is 2x. However, what if we rewrite x2 as the sum of x x's, and then take the derivative:

d/dx[ x2 ] = d/dx[ x + x + x + ... (x times) ]
= d/dx[x] + d/dx[x] + d/dx[x] ... (x times)
= 1 + 1 + 1 + ... (x times)
= x
This argument shows that the derivative of x2 with respect to x is actually x. So what's going on here?

Note: Most people with some math experience can show that some part of the argument is erroneous. As in simply, something doesn't follow. However, a full solution will explain why this argument attacks something that lies at the very heart of calculus itself, and that is what really explains why it's erroneous.

VANISHING DOLLAR

Three men go to a cheap motel, and the desk clerk charges them a sum of $30.00 for the night. The three of them split the cost ten dollars each. Later the manager comes over and tells the desk clerk that he overcharged the men, since the actual cost should have been $25.00. The manager gives the bellboy $5.00 and tells him to give it to the men. The bellboy, however, decides to cheat the men and pockets $2.00, giving each of the men only one dollar.

Now each man has paid $9.00 to stay for the night, and 3 x $9.00 = $27.00. The bellboy has pocketed $2.00. But $27.00 + $2.00 = $29.00. Where is the missing $1.00? WTF?

INFINITE QUARTER SEQUENCE

You are wearing a blindfold and thick gloves. An infinite number of quarters are laid out before you on a table of infinite area. Someone tells you that 20 of these quarters are tails and the rest are heads. He says that if you can split the quarters into 2 piles where the number of tails quarters is the same in both piles, then you win all of the quarters. You are allowed to move the quarters and to flip them over, but you can never tell what state a quarter is currently in (the blindfold prevents you from seeing, and the gloves prevent you from feeling which side is heads or tails). How do you partition the quarters so that you can win them all?

Hint 1: If an infinite number of quarters confuses you, try 100.

Click here to see the answer

CAMEL BANANA TRANSPORT

You have 3,000 bananas and a camel which can carry at most 1,000 bananas at a time. The camel eats a banana before moving a unit. You want to transport the bananas 1,000 units. What is the maximum number of uneaten bananas that you can move 1,000 units?

TRIANGLIA

Trianglia is a jacked-up island where no road has a dead end, and all the crossroads are "Y" shaped. The young prince of Trianglia mounts his horse, and is about to go on a quest to explore the land of Trianglia. He gets to the road by his palace, when the mother queen comes out and shouts: "But Charles, how will you find your way back?". "Don't worry Elizabeth", the prince replies, "I will turn right in every second crossroad to which I arrive, and left otherwise. Thus I shall surely return to the palace sooner or later." Is the prince right?
explain

DAUGHTERS' AGES

Local Berkeley professors Dr. Demmel and Dr. Shewchuk bump into each other on Telegraph Ave. They haven't seen each other since Vietnam.

Shewchuk hey! how have you been?
Demmel great! i got married and i have three daughters now
Shewchuk really? how old are they?
Demmel 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..
Shewchuk right, ok ... oh wait ... hmm, i still don't know
Demmel oh sorry, the oldest one just started to play the piano
Shewchuk wonderful! my oldest is the same age!


How old are the daughters?

GREEDY PIRATES

A pirate ship captures a treasure of 1000 golden coins. The treasure has to be split among the 5 pirates: 1, 2, 3, 4, and 5 in order of rank. The pirates have the following important characteristics: infinitely smart, bloodthirsty, greedy. Starting with pirate 5 they can make a proposal how to split up the treasure. This proposal can either be accepted or the pirate is thrown overboard. A proposal is accepted if and only if a majority of the pirates agrees on it. What proposal should pirate 5 make?

CALENDAR CUBES I

a corporate business man has two cubes on his office desk. every day he arranges both cubes so that the front faces show the current day of the month. what numbers are on the faces of the cubes to allow this?

Note: You can't represent the day "7" with a single cube with a side that says 7 on it. You have to use both cubes all the time. So the 7th day would be "07". I also should note that this is a really sly problem. Almost unfair.


There are many solutions

THREE-WAY PISTOL DUEL

you're a cyborg in a pistol duel with two other cyborgs. you have been programmed to fire pistols with an accuracy of 33%. the other two cyborgs shoot with accuracies of 100% and 50%, respectively. the rules of the duel are one shot per-cyborg per-round. the shooting order is from worst shooter to best shooter. thus, you go first, the 50% guy goes second, and the 100% guy goes third; repeat. if a cyborg dies, we just skip his or her turn, obviously. what should you shoot at in round 1 to maximize your chances of survival over time?

5 CARD MAGIC TRICK

this is a magic trick performed by two magicians, A and B, with one regular, shuffled deck of 52 cards. A asks a member of the audience to randomly select 5 cards out of a deck. the audience member -- who we will refer to as C from here on -- then hands the 5 cards back to magician A. after looking at the 5 cards, A picks one of the 5 cards and gives it back to C. A then arranges the other four cards in some way, and gives those 4 cards face down, in a neat pile, to B. B looks at these 4 cards and then determines what card is in C's hand (the missing 5th card). how is this trick done?

Note 1: There's no secretive message communication in the solution, like encoded speech or ninja hand signals or ESP or whatever ... the only communication between the two magicians is in the logic of the 4 cards transferred from A to B. Think of these magicians as mathematicians.

SQUARE FORMATION

Using all five of the pieces shown below, make a new square.

Save the image. then print it. Then cut out the pieces and play with them on your desk.

100 PRISONERS AND A LIGHT BULB

100 prisoners are imprisoned in solitary cells. Each cell is windowless and soundproof. There's a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb from his or her own cell. Each day, the warden picks a prisoner equally at random, and that prisoner visits the central living room; at the end of the day the prisoner is returned to his cell. While in the living room, the prisoner can toggle the bulb if he or she wishes. Also, the prisoner has the option of asserting the claim that all 100 prisoners have been to the living room. If this assertion is false (that is, some prisoners still haven't been to the living room), all 100 prisoners will be shot for their stupidity. However, if it is indeed true, all prisoners are set free and inducted into MENSA, since the world can always use more smart people. Thus, the assertion should only be made if the prisoner is 100% certain of its validity.

Before this whole procedure begins, the prisoners are allowed to get together in the courtyard to discuss a plan. What is the optimal plan they can agree on, so that eventually, someone will make a correct assertion?

Note 1: What is meant by optimal? If your solution is optimal, it means you can prove that no other algorithm can produce a lower average running time. This is usually very hard to do though, and I would be surprised if anyone ever sends me such a proof. So the best we can do in the meantime is try to beat the best average running time we know of. The number to beat so far is around 3500 days. So BEFORE YOU E-MAIL ME YOUR SOLUTION(a_red_Sani@yahoo.co.in), check its average time to see if beats the 4000 day ballpark. If you get a number around 27-28 years, then you've found the solution most people who solve the puzzle come up with. However, it's not optimal.

Note 2: How to compute average running time? The preferred method is to do a probabilistic analysis using pencil and paper. But if you haven't learned about stuff like that, a much simpler way is to just program your solution and run it maybe 100 times, recording how many days elapsed in each invocation. Afterwards you should have an array of 100 numbers. Now take the average of all them, and you'll have an empirical average which is close to the theoretical one.

Note 3: The problem statement used to say "The prisoners are allowed to get together one night to discuss a plan." In the forum, quite a few people mentioned the clever solution of simply having the planning meeting in the central living room, and then asserting that everyone has been there on the first day of the random selection process. To assure that this problem is not so easily defeated, I have stipulated that the meeting happen in the courtyard.

CIRCULAR JAIL CELL

There is a circular jail with 100 cells numbered 1-100. Each cell has an inmate and the door is locked. One night the jailor gets drunk and starts running around the jail in circles. In his first round he opens each door. In his second round he visits every 2nd door (2,4,6---) and shuts the door. In the 3rd round he visits every 3rd door (3,6,9---) and if the door is shut he opens it, if it is open he shuts it. This continues for 100 rounds (i.e. 4,8,12 ---; 5,10,15 ---; ---; 49,98 etc.) and exhausted the jailor falls down. How many prisoners found their doors open after 100 rounds?

BIRTHDAY TWINS

Sheila and He-Man are twins; Sheila is the OLDER twin. Assume they were born immediately after each other, an infinitesimally small - but nonzero - amount of time apart. During one year in the course of their lives, Sheila celebrates her birthday two days AFTER He-Man does. How is this possible?

10/28/2002 3:58AM Bonus: What is the maximum amount of time by which Sheila and He-Man can be apart in their birthday celebrations during the same year? I think it's more than two days.

Note: For both Sheila and He-Man, these birthday celebrations happen on the actual birthday date -- it cannot be a celebration that occurs at a date earlier or later than the actual birthday date for whatever reasons of convenience. Also, the solution has nothing to do with the theory of relativity or any other over complicated nonsense like that.

Doublespeak Proverbs

The following proverb brainteasers represent well known old sayings that have been relied on for hundreds of years. You've probably used these proverbs, or at least have heard them used at some point in your life. But for this brainteaser quiz, they have been re-written using BIG WORDS that mean essentially the same thing, but sound a whole lot different.

If you can translate these camouflaged (but familiar) witticisms, you have a talent for making clear writing out of doublespeak. We think you'll agree that they sound much better and make a lot more sense in their original forms, which relied on plain and simple English

1) Neophyte's serendipity.
2) The stylus is more potent than the claymore.
3) It is fruitless to indoctrinate a super-annuated canine with innovative manoeuvres.
4) The person presenting the ultimate cachinnation possesses, thereby, the optimal cachinnation.
5) Sorting on the part of mendicants must be interdicted.
6) Exclusive dedication to necessary chores without interludes of hedonistic diversion renders John a heptudinous fellow.
7) Pulchritude possesses solely cutaneous profundity
8) Where there are visible vapours having their province in ignited carbonaceous material, there is conflagration
9) A plethora of individuals with expertise in culinary techniques vitiates the potable concoction produced by steeping comestibles.
10) Male cadavers are incapable of yielding testimony.
11) All articles that coruscate with resplendence are not truly auriferous.
12) Members of an avian species of identical plumage congregate.
13) Eschew the implement of corrections and vitiate the scion.
14) If a large solid-hoofed mammal becomes available to you without compensation, refrain from casting your faculty for seeing into the oral cavity of such a creature.
15) Each vaporous mass suspended in the firmament has an interior decoration of metallic hue.
16) It is not advantageous to place the sum total of your barnyard collections into the same wicker receptacle
17) Feathered bipeds of a kindred mind in their segregated environment associate with a high degree of amiability.
18) Deviation from the ordinary or common routine of existence is that which gives zest to man's cycle of existence.
19) He who locks himself into the arms of Morpheus promptly at eventide, and starts the day before it is officially announced by the rising sun, excels in physical fitness, increases his economic assets and celebrates with remarkable efficiency.
20) Do not traverse a structure erected to afford passage over a waterway until the time of drawing nigh unto it.
21) Superfluous chronological dispatch institutes riddance of value defects.
22) There’s no value to be derived from demanding attention by loud screeches over fallen white liquid derived from the lactic glands of a female bovine.
23) An excess of culinary experts impairs the quality of a thin derivative of meat.
24) A body of persons abiding in a domicile of silica combined with metallic oxides should not carelessly project small geological specimens.

Introducing "Challenge Questions"

Every week we are gonna post one Challenge question starting from 15th June and the winner( the person who gets the correct answer) will be rewarded with free goodies(the goodies will depend on the Blogs earnings). so the more we earn the more GET so share the blog with your friends.

Terms and conditions -:
1) in case of a tie there will be a lucky draw where the the answer which was givin will be given priority.
2) All answers have to be sent to a_red_sani@yahoo.co.in and should have the topic "Challenge question no - ## ")
3) The decision of the blog is final
4) Multiple entries are not allowed
5) You need to prove ur identity to receive the reward
6) your answer should contain
a) name
b) age
c) gender
d) contact info

POPULATION OF FUNKYTOWN

In the city of Funkytown, the following facts are true:

No two inhabitants have exactly the same number of hairs.
No inhabitant has exactly 483,207 hairs.
There are more inhabitants than there are hairs on the head of any one inhabitant.
What is the largest possible number of inhabitants of Funkytown?

PAPER CUTTING


You have a 5x5 piece of paper. Two diagonally opposite corners of this paper are truncated as shown in the diagram below. You also have scissors. Show how to cut up the 5x5 paper into two pieces, so that the two pieces can then be interlocked to form a 6x4 rectangle.

LIGHT BULBS AND SWITCHES

You are in a room with three light switches, each of which controls one of three light bulbs in the next room. Your task is to determine which switch controls which bulb. All lights are initially off, and you can't see into one room from the other. You are allowed only one chance to enter the room with the light bulbs. How can you determine which lightswitch goes with which light bulb?

EQUILATERAL TRIANGLE DIVISION

draw an equilateral triangle (all sides same length). divide it into four identical shapes. remove the bottom left hand shape. now divide the resulting shape into four identical shapes.

SQUARE DIVISION

draw a square. divide it into four identical squares. remove the bottom left hand square. now divide the resulting shape into four identical shapes.

GHETTO ENCRYPTION II

Three coworkers would like to know their average salary. However, they are self-conscious and don't want to tell each other their own salaries, for fear of either being ridiculed or getting their houses robbed. How can they find their average salary, without disclosing their own salaries? and there is no other person computer or any type of gadget
and these guys are mathematicians and will do anything to get to know others income

GHETTO ENCRYPTION I

You want to send a valuable object to a friend securely. You have a box which can be fitted with multiple locks, and you have several locks and their corresponding keys. However, your friend does not have any keys to your locks, and if you send a key in an unlocked box, the key could be copied en route. How can you send the object securely?

Alternative, more precise phrasing: Andy and Grant are staying in different rooms in the same hotel. Andy needs to give a gold pendant to Grant, but spies are trying to assassinate Andy and Grant so neither of them can leave their room. The only way they can transfer objects is by using the bellhops. Both Andy and Grant have a safe with a large clasp that can be secured with a padlock. Both Andy and Grant have a padlock and a corresponding key. (So 1 gold pendant, 2 safes, 2 padlocks, and 2 keys.) But the bellhops are thieves. Anything that is not padlocked in the safe will be stolen by the bellhops - including any unlocked padlocks, the keys or the pendant. How can Andy transfer the gold pendant to Grant without it being stolen? (where both sides have encryption capability, and where unsecured items are taken away rather than just copied?)

GLOBE TRAVERSAL

how many places are there on the earth that one could walk one mile south, then one mile west, then one mile north and end up in the same spot? to be precise, let's assume the earth is a solid smooth sphere, so oceans and mountains and other such things do not exist. you can start at any point on the sphere. also, the rotation of the earth has nothing to do with the solution; you can assume you're walking on a static sphere if that makes the problem less complicated to you.


Get solution here

Wednesday, June 29, 2011

WHO AM I? (10)

The person who makes it, sells it. The person who buys it never uses it and the person who uses it doesn't know they are. What is it?


Get solution now just for a tweet

WHO AM I? (9)

Think of words ending in -GRY. Angry and hungry are two of them. There are only three words in the English language. What is the third word? The word is something that everyone uses every day. If you have listened carefully, I have already told you what it is.

Get solution now

WHO AM I? (8)

What is in seasons, seconds, centuries and minutes but not in decades, years or days?


Get solution now

WHO AM I? (7)

There was a green house. Inside the green house there was a white house. Inside the white house there was a red house. Inside the red house there were lots of babies. What is it?

Get solution now

WHO AM I? (6)

At night they come without being fetched. By day they are lost without being stolen. What are they?

Get solution now

WHO AM I? (5)

I never was, am always to be. No one ever saw me, nor ever will. And yet I am the confidence of all, To live and breath on this terrestrial ball. What am I?

Get solution now

WHO AM I? (4)

What always runs but never walks, often murmurs, never talks, has a bed but never sleeps, has a mouth but never eats?

Get solution now

WHO AM I? (3)

I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?

Get solution now

WHO AM I? (2)

It walks on four legs in the morning, two legs at noon and three legs in the evening. What is it?

Get solution now

WHO AM I? (1)

I am greater than God, and more evil than the devil. Poor people have me. Rich people want me. And if you eat me, you'll die. What am I?


Get solution now

COIN UNBIASING

You and your arch rival are competing for the same girl. After years of battling, you both decide to settle it by tossing a coin.

Your rival produces a coin, but you don't happen to have one on you. You are certain that the coin your rival has produced is loaded, ie. it will come up with heads more than 50% of the time on average.

How do you arrange a fair contest, based purely on chance and not skill, by flipping this coin?

Variation: (COIN BIASING) You and your rival are competing for the same girl, and decide to settle it with a coin toss. Your rival has known the girl longer than you have, so you agree that it is fair for him to have a chance of winning equal to P, where P > 0.5. However, you only have a fair coin. How can you conduct this contest such that the biased probability is manifested? What is the average number of coin flips needed to determine a winner?


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KNIGHT VS. DRAGON

A dragon and knight live on an island. This island has seven poisoned wells, numbered 1 to 7. If you drink from a well, you can only save yourself by drinking from a higher numbered well. Well 7 is located at the top of a high mountain, so only the dragon can reach it.

One day they decide that the island isn't big enough for the two of them, and they have a duel. Each of them brings a glass of water to the duel, they exchange glasses, and drink. After the duel, the knight lives and the dragon dies.

Why did the knight live? Why did the dragon die?

Get solution now

MYSTERIOUS TRIANGLE AREA


The second triangle is formed by rearranging pieces used to create the first. Yet there is a strange gap in the second triangle. Has area vanished? Is the conservation of matter bogus? Explain this madness.

Get solution now

LOGICAL SIGNS I

You are an archaeologist that has just unearthed a long-sought pair of ancient treasure chests. One chest is plated with silver, and the other is plated with gold. According to legend, one of the two chests is filled with great treasure, whereas the other chest houses a man-eating python that can rip your head off. Faced with a dilemma, you then notice that there are inscriptions on the chests:

Silver Chest
This chest contains the python.


Gold Chest
One of these two inscriptions is true.

Based on these inscriptions, which chest should you open?

Get solution now

HOURGLASSES

You have two hourglasses: a 7 minute one and an 11 minute one. Using just these hourglasses, accurately time 15 minutes.

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ARAB SHEIKH CAMELS

An Arab sheikh is old and must will his fortune to one of his two sons. He makes a proposition. His two sons will ride their camels in a race, and whichever camel crosses the finish line last will win the fortune for its owner. During the race, the two brothers wander aimlessly for days, neither willing to cross the finish line. In desperation, they ask a wise man for advice. He tells them something; then the brothers leap onto the camels and charge toward the finish line. What did the wise man say?

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MARBLE JARS

you are a prisoner in a foreign land. your fate will be determined by a little game. there are two jars, one with 50 white marbles, and one with 50 black marbles. at this point, you are allowed to redistribute the marbles however you wish (e.g. swap a black marble with a white marble, etc.): the only requirement is that after you are done with the redistribution, every marble must be in one of the two jars. afterwards, both jars will be shaken up, and you will be blindfolded and presented with one of the jars at random. then you pick one marble out of the jar given to you. if the marble you pull out is white, you live; if black, you die. how should you redistribute the marbles to maximize the probability that you live; what is this maximum probability (roughly)?

Get solution now

Poisened Drink Puzzle

A rich old man has died. After his death, his children are surprised to learn that he has left all of his money to his oldest son Jeremiah, who loved him dearly, and ignored his other children, who hated him.

So, the funeral is a day or two later, and the other sons and daughters have decided to kill Jeremiah and take his inheritance. Since his father's death, Jeremiah has taken to drinking, and they know that, at the wake, he's going to be gulping down the liquor like it was nectar of the gods. So they decide to poison the drinks. One of the other sons, Wallace, tends bar, and gets the poison all ready.

So Jeremiah comes up, crying and depressed, and orders a scotch on the rocks. Wallace serves him one, and he chugs it down in two seconds. "Give me another." Wallace gives him a second glass of scotch, which he also drinks in a matter of moments. The other siblings are puzzled...the poison is fast-acting; Jeremiah should be convulsing on the floor and retching his guts out. Finally, fifteen minutes later, a rather inebriated and very much alive Jeremiah orders one last glass of scotch, but as Wallace hands it to him, he changes his mind and leaves, sobbing. The other siblings come over to Wallace, and wonder what's going on. They talk about what could have gone wrong for a few minutes, and figure the poison's harmless. So Wallace sips the drink he poured for Jeremiah, and is pronounced DOA thirty minutes later.

Why did Jeremiah live? (He had no immunity to the poison, he didn't know it was coming, and the poison was obviously deadly.)

Get solution now

Rungs under water puzzle

A boat has a ladder that has six rungs, each rung is one foot apart. The bottom rung is one foot from the water. The tide rises at 12 inches every 15 minutes. Assume high tide peaks in one hour.

When the tide is at it's highest, how many rungs are under water?

get solution now

Prime Number Upside down

If you type the prime 3217001 on a calculator and hold it upside down, you can read the word "IDOLIZE", provided you accept that '0' can be both "D" and "O". Are there any larger primes that become a meaningful word when read upside down like this?

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The count puzzle

The puzzle is too simple, you just need to fill in the blanks below.
The number of 0 in this whole puzzle is ......
The number of 1 in this whole puzzle is ......
The number of 2 in this whole puzzle is ......
The number of 3 in this whole puzzle is ......
The number of 4 in this whole puzzle is ......
The number of 5 in this whole puzzle is ......
The number of 6 in this whole puzzle is ......
The number of 7 in this whole puzzle is ......
The number of 8 in this whole puzzle is ......
The number of 9 in this whole puzzle is ......

Get solution now

Lateral Thinking - The Elevator Puzzle

A man lives on the twelfth floor of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator -- or if it was raining that day -- he goes back to his floor directly. Otherwise, he goes to the tenth floor and walks up two flights of stairs to his apartment.

Why does the person follow such a way to go to his apartment?

Get solution now

Prisoner's Hat Puzzle

Four prisoners are caught and are to be punished. The judge allows them to be freed if they can solve a puzzle. If they do not, they will be hanged. They all agree.

The four prisoners are lined up on some steps (shown below). They are all facing in the same direction. A wall separates the fourth prisoner from the other three.



To summarize:-
Man 1 can see men 2 and 3.
Man 2 can see man 3.
Man 3 can see none of the others.
Man 4 can see none of the others.

The prisoners are wearing hats. They are told that there are two white hats and two black hats. The men initially don't know what colour hat they are wearing. They are told to shout out the color of the hat that they are wearing as soon as they know for certain what colour it is.

They are not allowed to turn round or move.
They are not allowed to talk to each other.
They are not allowed to take their hats off.
Who is the first person to shout out and why?



Difficult form of the puzzle -:
A group of N players, at least 3, are each wearing a hat. The hats are coloured black and white, and there is at least one hat of each colour. Each player can see the colour of every other player's hat, but not that of their own. Without communicating with any other player, some of the players must make a guess as to the colour of their hat. How accurate can the guesses of the players be?
The answer to this question depends on how the players are expected to make their guesses.


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Fork in the Road

A logician vacationing in the Bahamas finds himself on an island inhabited by two proverbial tribes of liars and truth-tellers. Members of one tribe always speak the truth, while other always lie. He stands at the fork of a road (a Tee-junction) and has to ask a bystander which leg he needs to follow to reach the village. He knows not whether the native is a truth-teller or a liar. The logician thinks for a moment and then asks only one question. What does he ask?

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License to Kill Puzzle

Inspector Ixolite of the Yard was investigating a murder at Nottonmye Manor. It was a difficult case, and Ixolite was completely stumped until he noticed a message sent to him by the killer cunningly hidden in a newspaper advertisement selling Car Licence Plates.
Inspector Ixolite thought about it for a while, and when he had solved the puzzle, immediately arrested the guilty man.

Now answer these :
Q1) How did Ixolite know the advert was a clue for him?
Q2) Solve the code and tell me who Ixolite arrested.

Following is the newspaper advert (Car license plates for sale) that Inspector Ixolite saw.

Plates For Sale
[W 05 NWO]
[H 13 HSR ]
[O 05 EBM]
[D 08 UNE]
[U 10 HTY]
[N 04 BRE]
[N 16 TTE]
[I 26 LHC ]
[T 10 AEE]
[I 26 CNA]
[X 22 VDA]


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Match and Lemon-aid Puzzle

A man in a restaurant asked a waiter for a juice glass, a dinner plate, water, a match, and a lemon wedge. The man poured enough water onto the plate to cover it.
"If you can get the water on the plate into this glass without touching or moving this plate, I will give you $100," the man said. "You can use the match and lemon to do this."
A few minutes later, the waiter walked away with $100 in his pocket. How did the waiter get the water into the glass?

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Poisoned Wine Puzzle

You are the owner of a renowned Wine catering services. You have a biggie offer of catering service to a party for the Queen of your place. So they have ordered a thousand bottles of wine (Yes a 1000!!!).
You are obviously so happy about it and worked hard to arrange the complete order. But suddenly tragedy occurred, one of you employee accidentally mixed a poisoned bottle with the wine bottles in the container. Being the same type of bottle you are not able to distinguish it without drinking and the death occurs in 24 hours after drinking.
The ceremony being tomorrow , the queen will order for your execution, if the order is not completed. Now you have to find a solution to it. You cannot have another 1000 bottles and you have to figure out that bottle. The queen takes care of this situation and tells you that you have 1000 prisoners to let them drink the bottles and find out the poisoned bottle.

Find the minimum number of prisoners required to find the poisoned bottle from the 1000 bottles in 24 hours!!

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