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?
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 proprietorfunnylogic
Presume that you do not know what a rhino looks like. Now the question goes like this: If one day while walking in a forest with two of your close friends, one friend shows you an elephant and tells that this is a rhino, and another friend shows you a hippopotamus and tells you that this is rhino, who would you believe and why?
I told you that you do not know what a rhino looks like, not that you are unaware of what a hippo and elephant look like. So you shouldn't believe either of them.logic
You're walking down a path and come to two doors. One of the doors leads to a life of prosperity and happiness, and the other door leads to a life of misery and sorrow. You don't know which door is which.
In front of the door is ONE man. You know that this man either always lies, or always tells the truth, but you don't know which. The man knows which door is which.
You are allowed to ask the man ONE yes-or-no question to figure out which door to go through. To make things more difficult, the man is very self-centered, so you are only allowed to ask him a question about what he thinks or knows; your question cannot involve what any other person or object (real or hypothetical) might say.
What question should you ask to ensure you go through the good door?
You should ask: "If I asked you if the good door is on the left, would you say yes?"
Notice that this is subtly different than asking "Is the good door on the left?", in that you are asking him IF he would say yes to that question, not what his answer to the question would be. Thus you are asking a question about a question, and if it ends up being the liar you are talking to, this will cause him to lie about a lie and thus tell the truth. The four possible cases are:
The man is a truth-teller and the good door is on the left. He will say "yes".
The man is a truth-teller and the good door is on the right. He will say "no".
The man is a liar and the good door is on the left. He will say "yes" because if you asked him "Is the good door on the left?", he would lie and say "no", and so when you ask him if he would say "yes", he will lie and say "yes".
The man is a liar and the good door is on the right. Similar to the previous example, he'll say "no".
So regardless of whether the man is a truth-teller or a liar, this question will get a "yes" if the door on the left is the good door, and a "no" if it's not.logic
You die and the devil says he'll let you go to heaven if you beat him in a game. The devil sits you down at a perfectly round table. He gives himself and you an infinite pile of quarters. He says, "OK, we'll take turns putting one quarter down, no overlapping allowed, and the quarters must rest flat on the table surface. The first guy who can't put a quarter down loses." You guys are about to start playing, and the devil says that he'll go first. However, at this point you immediately interject, and ask if you can go first instead. You make this interjection because you are very smart and can place quarters perfectly, and you know that if you go first, you can guarantee victory. Explain how you can guarantee victory.
You place a quarter right in the center of the table. After that, whenever the devil places a quarter on the table, mimic his placement on the opposite side of the table.. If he has a place to place a quarter, so will you. The devil will run out of places to put a quarter before you do. logicshort
Name the only sport in which the ball is always in possession of the team on defense, and the offensive team can score without touching the ball?
While mixing sand, gravel, and cement for the foundation of a house, a worker noticed a small bird hopping along the top of the foundation wall. The bird misjudged a hop and fell down one of the holes between the blocks. The bird was down too far for anyone to reach it and the hole was too small for it to fly out of. Someone suggested using two sticks to reach down into the hole and pull the bird out, but this idea was rejected for fear it would injure the fragile bird. What would be the easiest way to get the bird out of the hole without injuring it?
Since they had plenty of sand available, they could pour a little at a time into the hole. The bird would constantly keep shifting its position so that it stood on the rising sand.cleanlogic
Jake and his friend Paco had very famous challenge sessions at their school. One would suggest something they could do, and the other would prove it wrong somehow. One day, Jake surprised Paco by stating: "I can answer any question in the world." Sure that he would win the challenge, Paco accepted the task of proving it wrong. He wrote up a test full of impossible questions. After a while, Jake returned the test. Paco unbelievably lost the challenge and told Jake he could indeed answer any question. How did Jake win?
For all the impossible questions, Jake simply wrote "I don't know".logicmath
A grandfather's clock chimes the appropriate number of times to indicate the hour, as well as chiming once at each quarter hour. If you were in another room and hear the clock chime just once, what would be the longest period of time you would have to wait in order to be certain of the correct time?
You would have to wait 90 minutes between 12:15 and 1:45. Once you had heard seven single chimes, you would know that the next chime would be two chimes for 2 o'clock.logicmath
In the land of Brainopia, there are three races of people: Mikkos, who tell the truth all the time, Kikkos, who always tell lies, and Zikkos, who tell alternate false and true statements, in which the order is not known (i.e. true, false, true or false, true, false). When interviewing three Brainopians, a foreigner received the following statements:
I am a Mikko.
I am a Kikko.
a. They are both lying.
b. I am a Zikko.
Can you help the very confused foreigner determine who is who, assuming each person represents a different race?
Person 1 is a Miko.
Person 2 is a Ziko.
Person 3 is a Kikko. logic
Last week, the local Primary school was visited by the Government School Inspector who was there to check that teachers were performing well in their respective classes. He was very impressed with one particular teacher. The Inspector noticed that each time the class teacher asked a question, every child in the class put up their hands enthusiastically to answer it. More surprisingly, whilst the teacher chose a different child to answer the questions each time, the answers were always correct.
Why would this be?
The children were instructed to ALL raise their hands whenever a question was asked. It did not matter whether they knew the answer or not. If they did not know the answer, however, they would raise their LEFT hand. If they knew the answer, they would raise their RIGHT hand. The class teacher would choose a different child each time, but always the ones who had their RIGHT hand raised.