Riddle #670

logic

Two barbers

A man was in a small town for the day, and needed a haircut. He noticed that there were only two barbers in town, and decided to apply a bit of logical deduction to choosing the best one. Looking at their shops, he saw that the first one was very neat and the barber was clean shaven with a nice haircut. The other shop was a mess, and the barber there needed a shave and had a bad cut besides.Why did the man choose to go to the barber with the messy shop?
Since even barbers rarely try to cut their own hair, and there are only two barbers in town, they must cut each other's hair. The one with the neat hair must have it cut by the one with the bad haircut, who must then be better one, considering his own haircut.
91.22 %
48 votes

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logic

The genie and the wish

General Custer is surrounded by Indians and he's the only cowboy left. He finds an old lamp in front of him and rubs it. Out pops a genie. The genie grants Custer one wish, with a catch. He says, "Whatever you wish for, each Indian will get two of the same thing." Custer ponders a while and thinks:"If I get a bow and arrow they get two. If I get a rifle they get two!" He then rubs the bottle again and out pops the genie. "Well," the genie asks "have you made up your mind?" What did Custer ask for to help him get away?
One glass eye.
87.71 %
46 votes

logicmathprobability

The same birthday

What is the least number of people that need to be in a room such that there is greater than a 50% chance that at least two of the people have the same birthday?
Only 23 people need to be in the room. Our first observation in solving this problem is the following: (the probability that at least 2 people have the same birthday + the probability that nobody has the same birthday) = 1.0 What this means is that there is a 100% chance that EITHER everybody in the room has a different birthday, OR at least two people in the room have the same birthday (and these probabilities don't add up to more than 1.0 because they cover mutually exclusive situations). With some simple re-arranging of the formula, we get: the probability that at least 2 people have the same birthday = (1.0 - the probability that nobody has the same birthday) So now if we can find the probability that nobody in the room has the same birthday, we just subtract this value from 1.0 and we'll have our answer. The probability that nobody in the room has the same birthday is fairly straightforward to calculate. We can think of this as a "selection without replacement" problem, where each person "selects" a birthday at random, and we then have to figure out the probability that no two people select the same birthday. The first selection has a 365/365 chance of being different than the other birthdays (since none have been selected yet). The next selection has a 364/365 chance of being different than the 1 birthday that has been selected so far. The next selection has a 363/365 chance of being different than the 2 birthdays that have been selected so far. These probabilities are multiplied together since each is conditional on the previous. So for example, the probability that nobody in a room of 3 people have the same birthday is (365/365 * 364/365 * 363/365) =~ 0.9918 More generally, if there are n people in a room, then the probability that nobody has the same birthday is (365/365 * 364/365 * ... * (365-n+2)/365 * (365-n+1)/365) We can plug in values for n. For n=22, we get that the probability that nobody has the same birthday is 0.524, and thus the probabilty that at least two people have the same birthday is (1.0 - 0.524) = 0.476 = 47.6%. Then for n=23, we get that the probability that nobody has the same birthday is 0.493, and thus the probabilty that at least two people have the same birthday is 1.0 - 0.493) = 0.507 = 50.7%. Thus, once we get to 23 people we have reached the 50% threshold.
89.44 %
54 votes

logicmath

A hiking group are on a five day expedition

On the first day they cover one quarter of the total distance. The next day they cover one quarter of what is left. The following day they cover two fifths of the remainder and on the fourth day half of the remaining distance. The group now have 14 miles left, how many miles have they walked?
68.962962 miles
91.77 %
30 votes

funnylogic

Arrested in jail

Sam is talking to his lawyer in jail. They are very upset because the judge has refused to grant bail. At the end of the conversation Sam is allowed to leave the jail. Why?
Sam is visiting his lawyer, who had been arrested and jailed.
91.86 %
52 votes

funnylogicshort

Kicked off the train

A hobo had just been kicked off the train by one of the bosses. As he made his way down a dusty side road, he noticed a saffron robed man sitting next to a campfire apparently deep in thought. A wonderful smelling stew was bubbling in a pot next to him. It had been a full day since the hobo's last meal, so he went over to the man and tapped him on the shoulder. "I see by your robes that you are some kind of holy man," said the hobo. The Zen Master turned to the hobo and said, "You speak the truth." The hobo spoke, "I would sure like to try the stew you have on the campfire there; perhaps if I could tell you something to increase your wisdom, you will agree to share your meal." The Zen Master turned to the hobo and said, "Please, you are welcome to share my meal because you have already increased my wisdom!" What had the Zen Master learned from the hobo to increase his wisdom?
The Zen Master learned that he should find a more privace place to meditate if he doesn't want to be interrupted by every vagabond that happens by.
89.58 %
40 votes

logicmystery

Coin Toss

A dead body is found at the bottom of a multistory building. Seeing the position of the body, it is evident that the person jumped from one of the floors, committing suicide. A homicide detective is called to look after the case. He goes to the first floor and walks in the room facing the direction in which the body was found. He opens the window in that direction and flips a coin towards the floor. Then he goes to the second floor and repeats the process. He keeps on doing this until he reaches the last floor. Then, when he climbs down he tells the team that it is a murder not suicide. How did he come to know that it was a murder?
None of the windows were left open. If the person jumped, who closed the window?
74.39 %
107 votes

interviewlogic

Heaven’s Gate Problem

You are standing before two doors. One of the path leads to heaven and the other one leads to hell. There are two guardians, one by each door. You know one of them always tells the truth and the other always lies, but you don’t know who is the honest one and who is the liar. You can only ask one question to one of them in order to find the way to heaven. What is the question?
The question you should ask is “If I ask the other guard about which side leads to heaven, what would he answer?”. It should be fairly easy to see that irrespective of whom do you ask this question, you will always get an answer which leads to hell. So you can chose the other path to continue your journey to heaven. This idea was famously used in the 1986 film Labyrinth. Here is the explanation if it is yet not clear. Let us assume that the left door leads to heaven. If you ask the guard which speaks truth about which path leads to heaven, as he speaks always the truth, he would say “left”. Now that the liar , when he is asked what “the other guard (truth teller) ” would answer, he would definitely say “right”. Similarly, if you ask the liar about which path leads to heaven, he would say “right”. As the truth teller speaks nothing but the truth, he would say “right” when he is asked what “the other guard( liar ) ” would answer. So in any case, you would end up having the path to hell as an answer. So you can chose the other path as a way to heaven.
91.39 %
49 votes

cleanlogicshort

Party magician

Imagine John, a party magician, is carrying three pieces of gold each piece weighing one kilogram. While taking a walk he comes to a bridge which has a sign posted saying the bridge could hold only a maximum of 80 kilograms. John weighs 78 kilograms and the gold weighs three kilograms. John reads the sign and still safely crossed the bridge with all the gold. How did he manage this?
John is a juggler. When he came to the bridge he juggled the gold, always keeping one piece in the air.
87.19 %
44 votes