Suppose you want to send in the mail a valuable object to a friend. You have a box which is big enough to hold the object. The box has a locking ring which is large enough to have a lock attached and you have several locks with keys. However, your friend does not have the key to any lock that you have. You cannot send the key in an unlocked box since it may be stolen or copied. How do you send the valuable object, locked, to your friend - so it may be opened by your friend?
Send the box with a lock attached and locked. Your friend attaches his or her own lock and sends the box back to you. You remove your lock and send it back to your friend. You remove your lock and send it back to your friend. Your friend may then remove the lock she or he put on and open the box.
See also best riddles or new riddles.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.cleanlogicshort
What has a head and a tail, but no body?
There is a small town in the midwest with exactly 2 barbershops, one on each side of town. The barbershop on the west side of town is pristine. Its floors are spotless, the windows are always perfectly clear, and the air always smells fresh. The barber has a friendly smile, shined shoes, a well-groomed head of hair, and a fancy shirt. The barbershop on the east side of town is a mess. Its floors and windows are dirty, and the air smells of garbage. The barber always has a grimace on his face. His skin is oily, his hair is short and ragged, and he has food on his clothes all the time.
A man travelling through the town realizes he needs a haircut. Knowing the stories of the two barbers, the man decides to go to the dirty barbershop on the east side of town.
Why does he do this?
Because there are only two barbers in the town, the barbers must cut each-other's hair. The barber on the west side of town has a nice haircut, so the east-side barber must be a good barber. On the other hand, the barber on the east side of town has ragged hair, meaning the west-side barber must not be very good. So the man goes to the east-side barber to get a better haircut.logicmathprobability
You have a basket of infinite size (meaning it can hold an infinite number of objects). You also have an infinite number of balls, each with a different number on it, starting at 1 and going up (1, 2, 3, etc...).
A genie suddenly appears and proposes a game that will take exactly one minute. The game is as follows: The genie will start timing 1 minute on his stopwatch. Where there is 1/2 a minute remaining in the game, he'll put balls 1, 2, and 3 into the basket. At the exact same moment, you will grab a ball out of the basket (which could be one of the balls he just put in, or any ball that is already in the basket) and throw it away.
Then when 3/4 of the minute has passed, he'll put in balls 4, 5, and 6, and again, you'll take a ball out and throw it away.
Similarly, at 7/8 of a minute, he'll put in balls 7, 8, and 9, and you'll take out and throw away one ball.
Similarly, at 15/16 of a minute, he'll put in balls 10, 11, and 12, and you'll take out and throw away one ball.
And so on....After the minute is up, the genie will have put in an infinite number of balls, and you'll have thrown away an infinite number of balls.
Assume that you pull out a ball at the exact same time the genie puts in 3 balls, and that the amount of time this takes is infinitesimally small.
You are allowed to choose each ball that you pull out as the game progresses (for example, you could choose to always pull out the ball that is divisible by 3, which would be 3, then 6, then 9, and so on...).
You play the game, and after the minute is up, you note that there are an infinite number of balls in the basket.
The next day you tell your friend about the game you played with the genie. "That's weird," your friend says. "I played the exact same game with the genie yesterday, except that at the end of my game there were 0 balls left in the basket."
How is it possible that you could end up with these two different results?
Your strategy for choosing which ball to throw away could have been one of many. One such strategy that would leave an infinite number of balls in the basket at the end of the game is to always choose the ball that is divisible by 3 (so 3, then 6, then 9, and so on...). Thus, at the end of the game, any ball of the format 3n+1 (i.e. 1, 4, 7, etc...), or of the format 3n+2 (i.e. 2, 5, 8, etc...) would still be in the basket. Since there will be an infinite number of such balls that the genie has put in, there will be an infinite number of balls in the basket.
Your friend could have had a number of strategies for leaving 0 balls in the basket. Any strategy that guarantees that every ball n will be removed after an infinite number of removals will result in 0 balls in the basket.
One such strategy is to always choose the lowest-numbered ball in the basket. So first 1, then 2, then 3, and so on. This will result in an empty basket at the game's end. To see this, assume that there is some ball in the basket at the end of the game. This ball must have some number n. But we know this ball was thrown out after the n-th round of throwing balls away, so it couldn't be in there. This contradiction shows that there couldn't be any balls left in the basket at the end of the game.
An interesting aside is that your friend could have also used the strategy of choosing a ball at random to throw away, and this would have resulted in an empty basket at the end of the game. This is because after an infinite number of balls being thrown away, the probability of any given ball being thrown away reaches 100% when they are chosen at random.cleanfunnylogicshort
What can go up a chimney down but not down a chimney up?
One company had two factories, in different parts of the country, that were making the same style of shoes. In both factories, workers were stealing shoes. How, without using any security, could that company stop the stealing?
Make one factory make the left shoe, and the other make the right shoe.funnylogicshort
A woman depended on a public telephone to make her calls, but it was usually out of order. Each day she reported this to the phone company, but nothing was done. Finally she came up with a fib that she told the phone company. The phone was fixed the next day. What did she tell them?
She told them that people were making calls without having to pay.logic
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?
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.cleanlogic
You are standing next to three switches. You know these switches belong to three bulbs in a room behind a closed door – the door is tight closed, and heavy which means that it's absolutely impossible to see if any bulb is on or not. All three switches are now in position off.
You can do whatever you want with the switches and when you are finished you open the door and go into the room. While in there you have to tell which switch belongs to which bulb.
How will you do that?
Turn on the first switch and wait for a while. Turn off the first one and turn on the second. Go into the room. One bulb is shining, the second bulb is hot and the third one nothing.logicshort
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. High tide peaks in one hour. When the tide is at it's highest, how many rungs are under water?
None, the boat rises with the tide.