A king has 100 identical servants, each with a different rank between 1 and 100. At the end of each day, each servant comes into the king's quarters, one-by-one, in a random order, and announces his rank to let the king know that he is done working for the day. For example, servant 14 comes in and says "Servant 14, reporting in." One day, the king's aide comes in and tells the king that one of the servants is missing, though he isn't sure which one. Before the other servants begin reporting in for the night, the king asks for a piece of paper to write on to help him figure out which servant is missing. Unfortunately, all that's available is a very small piece that can only hold one number at a time. The king is free to erase what he writes and write something new as many times as he likes, but he can only have one number written down at a time. The king's memory is bad and he won't be able to remember all the exact numbers as the servants report in, so he must use the paper to help him. How can he use the paper such that once the final servant has reported in, he'll know exactly which servant is missing?
SEE ANSWER
When the first servant comes in, the king should write down his number. For each other servant that reports in, the king should add that servant's number to the current number written on the paper, and then write this new number on the paper.
Once the final servant has reported in, the number on the paper should equal
(1 + 2 + 3 + ... + 99 + 100) - MissingServantsNumber
Since (1 + 2 + 3 + ... + 99 + 100) = 5050, we can rephrase this to say that the number on the paper should equal
5050 - MissingServantsNumber
So to figure out the missing servant's number, the king simply needs to subtract the number written on his paper from 5050:
MissingServantsNumber = 5050 - NumberWrittenOnThePaper
A man and woman run through a field holding hands. They bound toward the sunset, happy as can be. Suddenly, the man moves off of his straight-line course and starts veering to his left. At the same time, the woman begins running off to her right.
They continue this for a full minute, but never let go of each others' hands. How is this possible?
Answer:- The man was facing forward, but the woman was running backwards. The man's right hand was holding the woman's right hand. They both veered in the same geographic direction, but it was the man's left and the woman's right because the woman was running backwards.
A man comes to a small hotel where he wishes to stay for 7 nights. He reaches into his pockets and realizes that he has no money, and the only item he has to offer is a gold chain, which consists of 7 rings connected in a row (not in a loop).
The hotel proprietor tells the man that it will cost 1 ring per night, which will add up to all 7 rings for the 7 nights.
"Ok," the man says. "I'll give you all 7 rings right now to pre-pay for my stay."
"No," the proprietor says. "I don't like to be in other people's debt, so I cannot accept all the rings up front."
"Alright," the man responds. "I'll wait until after the seventh night, and then give you all of the rings."
"No," the proprietor says again. "I don't like to ever be owed anything. You'll need to make sure you've paid me the exact correct amount after each night."
The man thinks for a minute, and then says "I'll just cut each of my rings off of the chain, and then give you one each night."
"I do not want cut rings," the proprietor says. "However, I'm willing to let you cut one of the rings if you must."
The man thinks for a few minutes and then figures out a way to abide by the proprietor's rules and stay the 7 nights in the hotel. What is his plan?
Answer:- The man cuts the ring that is third away from the end of the chain. This leaves him with 3 smaller chains of length 1, 2, and 4. Then, he gives rings to the proprietor as follows:
After night 1, give the proprietor the single ring
After night 2, take the single ring back and give the proprietor the 2-ring chain
After night 3, give the proprietor the single ring, totalling 3 rings with the proprietor
After night 4, take back the single ring and the 2-ring chain, and give the proprietor the 4-ring chain
After night 5, give the proprietor the single ring, totalling 5 rings with the proprietor
After night 6, take back the single ring and give the proprietor the 2-ring chain, totalling 6 rings with the proprietor
After night 7, give the proprietor the single ring, totalling 7 rings with the proprietor
A man had a book that was worth $40,000. There were only 2 books in existence. He threw it in the furnace, reducing it to a pile of soot. Why did he do this?
Answer:- He destroyed the book because he has two, and by only having one, the value goes up.
A man has two ropes of varying thickness (Those two ropes are not identical, they aren’t the same density nor the same length nor the same width). Each rope burns in 60 minutes. He actually wants to measure 45 mins. How can he measure 45 mins using only these two ropes.
He can’t cut the one rope in half because the ropes are non-homogeneous and he can’t be sure how long it will burn.
Answer:- 98
2+3=2*[3+(2-1)]=8
3+7=3*[7+(3-1)]=27
4+5=4*[5+(4-1)]=32
5+8=5*[8+(5-1)]=60
6+7=6*[7+(6-1)]=72
therefore
7+8=7*[8+(7-1)]=98
x+y=x[y+(x-1)]=x^2+xy-x
A man needs to send important documents to his friend across the country. He buys a suitcase to put the documents in, but he has a problem: the mail system in his country is very corrupt, and he knows that if he doesn't lock the suitcase, it will be opened by the post office and his documents will be stolen before they reach his friend.
There are lock stores across the country that sell locks with keys. The only problem is that if he locks the suitcase, he has no way to send the key to his friend so that the friend will be able to open the lock: if he doesn't send the key, then the friend can't open the lock, and if he puts the key in the suitcase, then the friend won't be able to get to the key.
The suitcase is designed so that any number of locks can be put on it, but the man figures that putting more than one lock on the suitcase will only compound the problem.
After a few days, however, he figures out how to safely send the documents. He calls his friend who he's sending the documents to and explains the plan.
What is the man's plan?
Answer:- The plan is this:
1. The man will put a lock on the suitcase, keep the key, and send the suitcase to his friend.
2. The friend will then put his own lock on the suitcase as well, keep the key to that lock, and send the suitcase back to the man.
3. The man will use his key to remove his lock from the suitcase, and send it back to the friend.
4. The friend will remove his own lock from the suitcase and get to the documents.
Search: Man-in-the-middle attack
A man puts on a clean shirt every night before bed. On the first nigh he puts on a blue shirt. He than sleeps for 5 hours. Every one hour more he sleeps than the night before he put on a different color shirt the next night according to this scale: blue, black, red, green, white, pink, orange, brown, purple, yellow, grey, neon green, tan, and teal. Every one hour less he sleeps than the last night he put on a different color shirt the next night going backwards on his scale.
If he were to wear a blue shirt because he slept more hours than the last night he does. If it was because he slept less hours than the night before he skips it and wears a teal shirt instead. If he goes backwards on the scale and goes to blue but would not wear a blue shirt he still counts blue in his going backwards on his scale.
The second night the man wears a blue shirt because he did not sleep any more or less hours than the last night. The man sleeps for six hours that night.
The next night he sleeps for five hours.
Night number four he sleeps for eight hours.
The next night he sleeps for seven hours.
The next night he sleeps so well he sleeps for 11 hours.
Night number seven he stays up so late he only sleeps for four hours.
The next night he is so tired he sleeps for eight hours.
The next night he sleeps for eight hours again.
Night number ten he sleeps for 14 hours because he is sick.
Since he slept so long the last night he only sleeps for seven hours.
The next night he is a little bit tired so he sleeps for eight hours.
The night after that he had to do so much work he only slept five hours.
The next night at work they let him out early and he slept for nine hours.
The next night he slept for eight hours.
And the last night the man did he slept for ten hours.
The next night he put on a different color shirt according to his scale, but the next night he randomly picked a shirt. At what night will the man wear a blue shirt again?
Answer:- Locker 1,000,000 will be open.
If you think about it, the number of times that each locker is flipped is equal to the number of factors it has. For example, locker 12 has factors 1, 2, 3, 4, 6, and 12, and will thus be flipped 6 times (it will end be flipped when you flip every one, every 2nd, every 3rd, every 4th, every 6th, and every 12th locker). It will end up closed, since flipping an even number of times will return it to its starting position. You can see that if a locker number has an even number of factors, it will end up closed. If it has an odd number of factors, it will end up open.
As it turns out, the only types of numbers that have an odd number of factors are squares. This is because factors come in pairs, and for squares, one of those pairs is the square root, which is duplicated and thus doesn't count twice as a factor. For example, 12's factors are 1 x 12, 2 x 6, and 3 x 4 (6 total factors). On the other hand, 16's factors are 1 x 16, 2 x 8, and 4 x 4 (5 total factors).
So lockers 1, 4, 9, 16, 25, etc... will all be open. Since 1,000,000 is a square number (1000 x 1000), it will be open as well.
A man was in a small town for the day, and needed a haircut. He noticed that there were only two barbers in town, and decided to apply a bit of logical deduction to choosing the best one. Looking at their shops, he saw that the first one was very neat and the barber was clean shaven with a nice haircut. The other shop was a mess, and the barber there needed a shave and had a bad cut besides. Why did the man choose to go to the barber with the messy shop?
Answer:- Since even barbers rarely try to cut their own hair, and there are only two barbers in town, they must cut each other's hair. The one with the neat hair must have it cut by the one with the bad haircut, who must then be better one, considering his own haircut.
A man was shot to death while in his car. There were no powder marks on his clothing which indicated that the gunman was outside the car. However, all the windows were up and the doors locked. After a close inspection was made, the only bullet holes discovered were on the man's body. How was he murdered?
Answer:- The victim was in a convertible.
A murdered is condemned to death.
He has to choose between three rooms.
The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven't eaten in 3 years.
Which room is safest for him?
Answer:- The third room. Lions that haven't eaten in three years are dead.
A new student met the Zen Master after traveling hundreds of miles by yak cart. He was understandably pleased with himself for being selected to learn at the great master's feet .
The first time they formally met, the Zen Master asked, "May I ask you a simple question?" "It would be an honor!" replied the student.
"Which is greater, that which has no beginning or that which has no end?" queried the Zen Master. "Come back when you have the answer and can explain why."
After the student made many frustrated trips back with answers which the master quickly cast off with a disapproving negative nod, the Zen Master finally said, "Perhaps I should ask you another question?"
"Oh, please do!" pleaded the exasperated student.
The Zen Master then asked, "Since you do not know that, answer this much simpler riddle. When can a pebble hold back the sea?" Again the student was rebuffed time and again. Several more questions followed with the same result. Each time, the student could not find the correct answer. Finally, completely exasperated, the student began to weep, "Master, I am a complete idiot. I can not solve even the simplest riddle from you!"
Suddenly, the student stopped, sat down, and said, "I am ready for my second lesson."
What was the Zen Master's first lesson?
Answer:- The student's first lesson was that in order to learn from the Zen Master, the student should be asking the questions and not the Zen Master.
A poor miller living with his daughter comes onto hard times and is not able to pay his rent. His evil landlord threatens to evict them unless the daughter marries him.
The daughter, not wanting to marry the landlord but fearing that her father won't be able to take being evicted, suggests the following proposition to the landlord. He will put two stones, one white and one black, into a bag in front of the rest of the townspeople. She will pick one stone out of the bag. If she picks the white stone, the landlord will forgive their debt and let them stay, but if she picks the black stone, she will marry the landlord, and her father will be evicted anyway.
The landlord agrees to the proposal. Everybody meets in the center of the town. The landlord picks up two stones to put in the bag, but the daughter notices that he secretly picked two black stones.
She is about to reveal his deception but realizes that this would embarrass him in front of the townspeople, and he would evict them. She quickly comes up with another plan. What can she do that will allow the landlord save face, while also ensuring that she and her father can stay and that she won't have to marry the landlord?
Answer:- The daughter picks a stone out, keeps it in her closed hand, and proclaims "this is my stone." She then throws it to the ground, and says "look at the other stone in the bag, and if it's black, that means I picked the white stone." The landlord will reveal the other stone, which is obviously black, and the daughter will have succeeded. The landlord was never revealed as a cheater and thus was able to save face.
A rich man's son was kidnapped. The ransom note told him to bring a valuable diamond to a phone booth in the middle of a public park. Plainclothes police officers surrounded the park, intending to follow the criminal or his messenger. The rich man arrived at the phone booth and followed instructions but the police were powerless to prevent the diamond from leaving the park and reaching the crafty villain. What did he do?
Answer:- This is a true story from Taiwan. When the rich man reached the phone booth he found a carrier pigeon in a cage. It had a message attached telling the man to put the diamond in a small bag which was around the pigeon's neck and to release the bird. When the man did this the police were powerless to follow the bird as it returned across the city to its owner.
A wise man lived on a hill above a small town. The townspeople often approached him to solve their difficult problems and riddles. One day, two lads decided to fool him. They took a dove and set off up the hill. Standing before him, one of the lads said "Tell me, wise man, is the dove I hold behind my back dead or alive?" The man smiled and said "I cannot answer your question correctly". Even though the wise man knew the condition of the dove, why wouldn't he state whether it was dead or alive?
Answer:- The man told the two lads, "If I say the dove is alive, you will the bird and show me that it is dead. If I say that it is dead, you will release the dove and it will fly away. So you see I cannot answer your question.
Search: Schrödinger's cat