A 400 yard long train, travelling at 30 mph, enters a 4.5 mile long tunnel.
How long will elapse between the moment the front of the train enters the tunnel and the moment the end of the train clears the tunnel?
A doctor and a bus driver are both in love with the same woman, an attractive girl named Sarah. The bus driver had to go on a long bustrip that would last a week. Before he left, he gave Sarah seven apples. Why?
Jay escaped from jail and headed to the country. While walking along a rural road, he saw a police car speeding towards him. Jay ran toward it for a short time and then fled into the woods. Why did he run toward the car?
Jay was just starting to cross a bridge when he saw a police car. He ran toward the car to get off the bridge before running into the woods.
At a dinner party, many of the guests exchange greetings by shaking hands with each other while they wait for the host to finish cooking.
After all this handshaking, the host, who didn't take part in or see any of the handshaking, gets everybody's attention and says: "I know for a fact that at least two people at this party shook the same number of other people's hands."
How could the host know this? Note that nobody shakes his or her own hand.
Assume there are N people at the party.
Note that the least number of people that someone could shake hands with is 0, and the most someone could shake hands with is N-1 (which would mean that they shook hands with every other person).
Now, if everyone at the party really were to have shaken hands with a different number of people, then that means somone must have shaken hands with 0 people, someone must have shaken hands with 1 person, and so on, all the way up to someone who must have shaken hands with N-1 people. This is the only possible scenario, since there are N people at the party and N different numbers of possible people to shake hands with (all the numbers between 0 and N-1 inclusive).
But this situation isn't possible, because there can't be both a person who shook hands with 0 people (call him Person 0) and a person who shook hands with N-1 people (call him Person N-1). This is because Person 0 shook hands with nobody (and thus didn't shake hands with Person N-1), but Person N-1 shook hands with everybody (and thus did shake hands with Person 0). This is clearly a contradiction, and thus two of the people at the party must have shaken hands with the same number of people.
Pretend there were only 2 guests at the party. Then try 3, and 4, and so on. This should help you think about the problem.
Search: Pigeonhole principle
This guy living on the 20th floor in an apartment building got up early each morning to go to work in a downtown store. He always went into the elevator on the 20th floor and rode down to the entrance (1st floor). When he came home he always rode the elevator from the entrance and up to the 8th floor. He walked out of the elevator and walked the stairs up to his apartment on the 20th floor. Why didn't he take the elevator all the way up to his apartment?
This guy is midget and can only reach to the 8th floor button.
