Hard riddles

logic

Headwaiter in a restaurant

Betty signals to the headwaiter in a restaurant, and says, ''There is a fly in my tea.'' The waiter says ''No problem Madam. I will bring you a fresh cup of tea.'' A few minutes later Betty shouts, ''Get me the manager! This is the same cup of tea.'' How did she know? Hint: The tea is still hot.
Betty had already put sugar in her tea before sending it back. When the "new" cup came, it was already tasted sweet.
86.62 %
42 votes

interviewlogicmath

Ant and Triangle Problem

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
86.32 %
41 votes

logicmath

One equals two

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.
86.32 %
41 votes

logic

King's riddle

Allan, Bertrand, and Cecil were caught stealing so the king sent them to the dungeon. But the king decided to give them a chance. He mad them stand in a line and put hats on their heads. He told them that if they answer a riddle, they could go free. Here is the riddle: "Each of you has a hat on your head. You do not know the color of the hat on your own head. If one of you can guess the color of the hat on your head, I will let you free. But before you answer you must keep standing in this line. You cannot turn around. Here are my only hints: there are only black and white hats. At least one hat is black. At least one hat is white." Allan couldn't see any hats. Bertrand could see Allan's hat but not his own. Cecil could see Bertrand's hat and Allan's hat, but not his own. After a minute nobody had solved the riddle. But then a short while later, one of them solved the riddle. Who was is and how did he know?
Bertrand knew the answer because Cecil didn't say anything after one minute. If Bertrand and Allan's hats were both the same color, then Cecil would know what color his hat was. But Cecil didn't know. So Bertrand knew that Allan's hat was a different color than his. Since Allan's hat was black, Betrand knew his hat was white.
85.53 %
58 votes

logic

Pink Island

It was a Pink Island. There were 201 individuals lived in the island. Among them 100 people were blue eyed people, 100 were green eyed people and the leader was a black eyed one. Except the leader, nobody knew how many individuals lived in the island. Neither have they known about the color of the eyes. The leader was a very strict person. Those people can never communicate with others. They even cannot make gestures to communicate. They can only talk and communicate with the leader. It was a prison for those 200 individuals. However, the leader provided an opportunity to leave the island forever but on one condition. Every morning he questions the individuals about the color of the eyes! If any of the individuals say the right color, he would be released. Since they were unaware about the color of the eyes, all 200 individuals remained silent. When they say wrong color, they were eaten alive to death. Afraid of punishment, they remained silent. One day, the leader announced that "at least 1 of you has green eyes! If you say you are the one, come and say, I will let you go if you are correct! But only one of you can come and tell me!" How many green eyed individuals leave the island and in how many days?
All 100 green eyed individuals will leave in 100 days. Consider, there is only one green eyed individual lived in the island. He will look at all the remaining individuals who have blue eyes. So, he can get assured that he has green eyes! If there were more than one green eyed people, when the first man looks at the second one with green eyes, the person didn’t leave on day the first day. It means he also has green eyes and the same rule applies to each green eyed man.
85.39 %
48 votes

logicprobability

Red and blue marbles

Your friend shows you two jars, one with 100 red marbles in it, the other with 100 blue marbles in it. He proposes a game. He'll put the two jars behind his back and tell you to pick one of them at random. You'll then close your eyes, he'll hand you the jar you picked, and you'll pick a random marble from that jar. You win if the marble you pick is blue, and you lose otherwise. To give you the best shot at winning, your friend gives you the two jars before the game starts and says you can move the marbles around however you'd like, as long as all 200 marbles are in the 2 jars (that is, you can't throw any marbles away). How should you move the marbles around to give yourself the best chance of picking a blue marble?
Put one blue marble in one jar, and put the rest of the marbles in the other jar. This will give you just about a 75% chance of picking a blue marble.
85.39 %
48 votes

cleanfunnyinterview

I know almost every song that has ever existed

A man is sitting in a pub feeling rather poor. He sees the man next to him pull a wad of £50 notes out of his wallet. He turns to the rich man and says to him, 'I have an amazing talent; I know almost every song that has ever existed.' The rich man laughs. The poor man says, 'I am willing to bet you all the money you have in your wallet that I can sing a genuine song with a lady's name of your choice in it.' The rich man laughs again and says, 'OK, how about my daughter's name, Joanna Armstrong-Miller?' The rich man goes home poor. The poor man goes home rich. What song did he sing?
Happy Birthday.
85.29 %
57 votes