A boy was rushed to the hospital emergency room. The ER doctor saw the boy and said, "I cannot operate on this boy. He is my son."
But the doctor was not the boy's father. How could that be?
A man was to be sentenced, and the judge told him, "You may make a statement. If it is true, I'll sentence you to four years in prison. If it is false, I'll sentence you to six years in prison." After the man made his statement, the judge decided to let him go free.What did the man say?
He said, "You'll sentence me to six years in prison." If it was true, then the judge would have to make it false by sentencing him to four years. If it was false, then he would have to give him six years, which would make it true. Rather than contradict his own word, the judge set the man free.
Every day, Jack arrives at the train station from work at 5 pm. His wife leaves home in her car to meet him there at exactly 5 pm, and drives him home. One day, Jack gets to the station an hour early, and starts walking home, until his wife meets him on the road. They get home 30 minutes earlier than usual. How long was he walking? Distances are unspecified. Speeds are unspecified, but constant. Give a number which represents the answer in minutes.
The best way to think about this problem is to consider it from the perspective of the wife. Her round trip was decreased by 30 minutes, which means each leg of her trip was decreased by 15 minutes. Jack must have been walking for 45 minutes.
Consider the following explanation for why 1=2:
1. Start out Let y = x
2. Multiply through by x xy = x2
3. Subtract y2 from each side xy - y2 = x2 - y2
4. Factor each side y(x-y) = (x+y)(x-y)
5. Divide both sides by (x-y) y = x+y
6. Divide both sides by y y/y = x/y + y/y
7. And so... 1 = x/y + 1
8. Since x=y, x/y = 1 1 = 1 + 1
8. And so... 1 = 2
How is this possible?
Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not followinng basic mathematical rules, we are able to get strange results like these.
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.
A man is found dead in the desert. He is wearing only his underwear. Half of a straw is found nearby.
How did this man die?
The man was flying in a hot-air balloon with another man over the desert. The balloon started to go down because of excess weight. Both men would die if they ended up stranded in the desert, so they stripped down to their underwear and threw their clothes off the balloon to try to reduce the weight. Unfortunately, that didn't work well enough. So they drew straws to decide who would jump. The dead man pulled the short straw and jumped out of the balloon.
Dodge was staying with Cousin Jamie in Jamie's lakeside cabin. They were setting up Jamie's will. As Dodge was Jamie's closest living relative, much of Jamie's estate was being left to him. One day, Jamie went to Dr Dodge very disturbed. "Doctor," he began, "I have just found out that a man named Georgio wants to get me. He will be here very soon. Where will I go? Where can I hide? If he finds me in here, he will surely kill me. I do not have time to leave this clearing and go farther into the woods."
Dr Dodge thought for a moment, and then grabbed a 5' long bamboo pole, with a diameter the size of a quarter. "Jamie, follow me out to the lake. This lake is 4' deep. If you lie on the bottom of the lake and breathe through this pole, Georgio will never find you. I will be in the bulrushes with a shotgun, and I will shoot him when he comes. I will swim down to find you when he is gone." Jamie consented, and lay down on the bottom of the lake with the bamboo pole in his mouth. A few hours later, a ranger passed by. He found Jamie's body, dead. Dr Dodge told the police of the circumstance, and that Jamie had probably panicked, and died. Police arrested Dr Dodge, on the charges of murdering Jamie. Why?
The bamboo pole did not have any cracks or holes. Its opening was above water the whole time.
Jamie died of carbon dioxide poisoning. The pole was 5' long, but only the size of a quarter. The first time he breathed in, he breathed oxygen. When he exhaled, the air could not travel 5' before he breathed in again. He was just breathing what he exhaled. Before long, all he was breathing was carbon dioxide. He died of CO2 poisoning. Doctor Doge was the one who told him to use the pole, therefore the cause of his death. Dodge is a DOCTOR, and therefore knows about the CO2. Dodge did murder Jamie. His motive: the money in the will.
Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?
So let’s think this through. The ants can only avoid a collision if they all decide to move in the same direction (either clockwise or anti-clockwise). If the ants do not pick the same direction, there will definitely be a collision. Each ant has the option to either move clockwise or anti-clockwise. There is a one in two chance that an ant decides to pick a particular direction. Using simple probability calculations, we can determine the probability of no collision.
P(No collision) = P(All ants go in a clockwise direction) + P( All ants go in an anti-clockwise direction) = 0.5 * 0.5 * 0.5 + 0.5 * 0.5 * 0.5 = 0.25
A man was found dead with a cassette recorder in one hand and a gun in the other.
When the police came in, they immediately pressed the play button on the cassette.
He said "I have nothing else to live for. I can't go on," then the sound of a gunshot.
After listening to the cassette tape, the police knew that it was not a suicide, but a homicide.
How did they know?
If the man shot himself while he was recording, how did he rewind the cassette tape?
