Brain Teasers.
1 . A businessman, for personal reasons of his own, needs to gain access to a notorious but elusive thieves guild. After snooping around the city for a few days, he finally gets a tip about the location of the guild entrance down a dark alleyway. After observing the entrance for about an hour, the businessman notices that the thieves seem to have some sort of passcode system using numbers. When someone approaches the door, they are given a number, and then they reply with a number. The first person steps up, and the guard tells them "twelve," to which they respond "six." The person is admitted. A second person approaches the door, and the guard tells them "six," to which they reply "three." The second person is also admitted. Convinced that he has cracked the code, the businessman approaches the door to the thieves guild, and the guard tells him "ten," to which he confidently replies "five." The guard immediately slams the door in the businessman's face, and a deadbolt slots into place. It seems the businessman is not as clever as he thought. What is another way the numbers that the guard asked the first two people could produce the numbers they gave in reply?
2 . A farmer challenges an engineer, a physicist, and a mathematician to build him a fence that encloses the most area worldwide with the least amount of fencing. The engineer proposes to fence the entire country around its coast line. The physicist proposes a long straight line of fence and said the length was infinite around the equator, as fencing half the world was the most efficient way. Though the fence would be longer the area to fence ratio would be superior. The mathematician laughed at the others, and then proceeded to build the winning fence. What did he build? The mathematician builds a small circular fence around himself and declares himself on the outside.
3 . A waiter at a classy restaurant likes to play a game with his diners, offering them a challenge that will earn them a 50 percent discount if they can figure it out. If they fail, however, they promise to give the waiter a hefty 50 percent tip. One diner accepts the challenge, and the waiter brings out an empty glass, a match and striker, and a used wine cork, and he sets these in front of the customer. Then the waiter sets a plate in front of him that has enough water on it to cover the bottom of the plate.The waiter says to the diner, "if you can get the water into the glass without touching or moving the plate, using only the objects I have brought you, then you get 50 percent off your meal tonight." This diner turned out to be pretty sharp, and he walked out with a 50 percent discount after his meal. What did he do?
4 . You are sitting in a rowboat on a small lake. You have a lead brick in your boat. You toss the brick out of your boat into the lake, where it quickly sinks to the bottom. Does the water level of the lake rise slightly, drop slightly, or stay the same?
5 . Every day at noon an ocean liner leaves London to sail for New York, and (simultaneously) an ocean liner sails from New York to London. The crossing takes exactly seven days and seven nights in either direction. How many other ocean liners will an ocean liner leaving London today pass at sea before arriving in New York?