Puzzles

On an island in the middle of the ocean lives several people of a peculiar sort: They are all logicians. One hundred of them have blue eyes, while the rest have brown eyes. The leader of the group, known as the guru, has green eyes. It so happens that no one on this island knows the color of their own eyes. At midnight every night a ferry arrives at the island, and leaves shortly thereafter with anyone who can tell the ferryman their eye color. ...

Four people are walking in the dark, and they have only one torch. They stumble upon a long and narrow bridge, which they need to cross. To cross the bridge they need the torch, and once it has been carried to the far side, someone needs to bring it back to the ones who are waiting. Only two can cross the bridge at the same time. One of the group is quite slow and takes 10 minutes to cross the bridge. The others take 5, 2 and 1 minutes, respectively. ...

As people die they sometimes go to hell. The devil, the nice bloke that he is, gives them a chance to escape and go to heaven. He lines them up outside the gates of hell and gives them each a black or white, with colors distributed randomly. No one gets to see the color of their own hat, but they can see the hats of everyone in front of them. ...

A farmer with a goat, a cabbage, and a wolf is standing on the side of a river. They need to cross it, but there is only a small row boat which only fits two of them. The goat is hungry, so if the farmer leaves the goat alone with the cabbage, the goat will eat the cabbage. The wolf is also hungry, and it will eat the goat if they are left alone. ...

You participate in a game show. In the final contest the host presents you with three doors. Behind one door is one million dollars. The other two hide sacks of potatoes. The host asks you to choose one door. After you have done so, the host will open one of the other doors, one hiding a sacks of potatoes. Now there are only two doors left - the one you’ve chosen, and one more. The host asks you: ...

Buffy thinks of a number, 1, 2 or 3. Willow is allowed to ask Buffy one yes-or-no question, to which she will answer “yes”, “no”, or, if she doesn’t know the answer, “I don’t know”. What question should Willow ask Buffy to uncover his number? Answer One solution is for Buffy to ask Willow: “I’m thinking of 1 or 2. Is your number higher than mine?” If Willow has 3, then she will answer “yes”. If she has 1, he must answer “no”. And, if she has 2, she can’t know if his number is higher than Buffy’s, so she must answer “I don’t know” ...

Variant 1 The well-renowned hotel of Bilzebab is famous for having an infinite number of rooms, and, being such a famous and well-renowned hotel, the hotel is occupied. Ten tourists arrive at the hotel and ask if there are any rooms available for them. Bilzebab is also famous for having a smart and quick-thinking manager. The manager thinks for a minute, and then says: “Yes, of course, I’ll just reorganize the current arrangements, and you will all get a room”. ...

As you walk along a path in a forest, the path splits in two. You do not know which way to go. At the junction, two solemn guards stand, ready to help any passersby. It so happens that the guards only know the words yes and no. It also happens to be that the guards are twin brothers, impossible to tell apart. And, as twin brothers, the guards have developed a quite peculiar dynamic: One of them always tells the truth, while the other always lies. ...

Five pirates have found a treasure chest containing one hundred coins, and are now in the process of dividing the treasure amongst themselves. In their usual democratic fashion they decide that the oldest of them will decide on how split up the treasure. After he has made his decision they will all vote to accept or reject his plan. If at least half of them vote to reject the plan, the oldest pirate gets thrown overboard, and the process is restarted with the next-to-oldest coming up with the plan, and so on. ...

Rebecca and her partner attend an evening party together with four other couples. During the initial mingling, everyone greets and shakes hands with those they hadn’t met before. Later in the evening Rebecca asks all nine other party-goers how many people they shook hands with, and she gets nine different answers. How many people did Rebecca shake hands with? Please note that everyone had met their partner prior to the party, and that no one shook hands with themselves. ...

There are ten piles of coins, and ten coins in each pile. Each coin in each pile weighs 1 gram, except for one pile where the coins weigh 1.1 grams. You have a digital scale, and you are allowed one attempt at using it. You can take any number of coins from any number of piles. How do you determine which pile has the heavier coins? Answer You take one coin from the first pile, two coins from the second pile, and so on until the ninth pile, from which you take nine coins. When you put these on the scale, look at the first number after the decimal point. If it shows a one, then you know that the coins in the first pile weighs more, and so on. If it shows a zero, then pile ten is the answer. ...

A girl leaves her home in the morning for school. She looks for the time on an old-fashioned, analog clock, through a mirror. Unfortunately there are no digits on the clock, so she mistakes the mirror image for the actual time. She rides her bike to school, which takes twenty minutes. When she arrives and looks at the school clock, it shows a time two-and-a-half hours later than the mirror image she saw at home. ...

You have three boxes in front of you, one with nails in it, one with screws, and one with both nails and screws. The boxes all have labels describing their contents. Unfortunately, all labels are incorrect, and describes one of the other boxes. You can pick up one item from one of the boxes (no peeking). How do you determine what is in each box? Put another way: From which box, with which label, do you take an item? ...

The great town wizard needs a new apprentice, and has announced a competition for the post. Many applicants have tried, and only the three brightest remain for the final challenge. The wizard gives each applicant a hat, and tells them that they have either a black or a white hat. The first one to figure out the color of her own hat and publicly announce it wins the challenge, and becomes the wizard’s apprentice. Also, if any of them sees another applicant having a white hat, they are supposed to say: ...

There are three lockers, each with two drawers. Each drawer contains one item - a pearl, or a clump of coal. In one locker both drawers contain pearls, in another both drawers contain clumps of coal, and in a the third locker one drawer contains a pearl, and the other contains a clump of coal. You do not know which locker is which. You open one drawer and find a pearl. If you are allowed to open one more drawer, which one should you open to maximise your chances of finding another pearl? ...

An old-fashioned light bulb hangs from the ceiling of an otherwise empty room. A door leads outside, where three switches sit on the wall. One of the switches control the light bulb - how do you figure out which switch it is? You cannot see from outside the room if the light bulb is on or off, and you are only allowed to enter the room once. The light bulb and all the switches are initially in their off position. You are allowed to flip the switches any number of times, and you can take as long as you want before answering. ...

Variant 1 You have eight small stone balls, where one is slightly heavier than the others. You have an old-fashioned balancing scale. In as few weighings as possible, how do you find the heavier ball? Answer You need two weighings. First, weigh three balls against three balls. If they balance, the heavier is one of the remaining two, which you can find in the next weighing. Otherwise, one side was heavier in the first weighing, and one of those three balls must be heavier. For the second weighing, take two of those prospects and weigh them. If they balance, the one left out is heavier. If they don’t balance, one of them is heavier, and it is the answer. ...