Logical Puzzles

Three friends Pablo, Edvard, and Henri are talking to each other about the art collection of Leonardo. Pablo says: "Leonardo has at least four paintings of Rembrandt." Edvard says: "No, he has less than four paintings of Rembrandt." "According me," says Henri, "Leonardo has at least one Rembrandt."

A man has a wolf, a goat, and a cabbage. He must cross a river with the two animals and the cabbage. There is a small rowing-boat, in which he can take only one thing with him at a time. If, however, the wolf and the goat are left alone, the wolf will eat the goat. If the goat and the cabbage are left alone, the goat will eat the cabbage.

In your bedroom you have a drawer with 2 red, 4 yellow, 6 purple, 8 brown, 10 white, 12 green, 14 black, 16 blue, 18 grey, and 20 orange socks. It is dark in your bedroom, so you can't distinguish between the colors of the socks.

Here are three answers:

1. Answer A
2. Answer A or B
3. Answer B or C

In the middle of a round pool lies a beautiful water-lily. The water-lily doubles in size every day. After exactly 20 days the complete pool will be covered by the lily.

You are standing next to a well, and you have two jugs. One jug has a content of 3 liters and the other one has a content of 5 liters.

The following four cards sit on a table:

Each card has a digit on one side and a letter on the other side.

Martin has one of the numbers 1, 2, or 3 in mind. Sophie is allowed to ask one question to Martin to find out which of these three numbers he has in mind. Martin will answer this question only with the answers "yes", "no", or "I don't know".

A rather silly car thief stole, without knowing it, the car of the chief of police. The police immediately started an investigation and on the basis of witness depositions, four suspects were arrested that were seen near the car at the time of the crime. Because the chief of police took the case very seriously, he decided to examine the suspects personally and use the new lie-detector of the police station. Each suspect gave three statements during the examinations, that are listed below:

Suspect A:

1. In high-school I was in the same class as suspect C.
2. Suspect B has no driving license.
3. The thief didn't know that it was the car of the chief of police.

Suspect B:

1. Suspect C is the guilty one.
2. Suspect A is not guilty.
3. I never sat behind the wheel of a car.

Suspect C:

1. I never met suspect A until today.
2. Suspect B is innocent.
3. Suspect D is the guilty one.

Suspect D:

1. Suspect C is innocent.
2. I didn't do it.
3. Suspect A is the guilty one.

With so many contradicting statements, the chief of police lost track. To make things worse, it appeared that the lie-detector didn't quite work yet as it should, because the machine only reported that exactly four of the twelve statements were true, but not which ones.

David and Angela play a game of tick-tack-toe. In this game, the players try to get three circles or three crosses in a row (horizontal, vertical, or diagonal).

They follow the following rules:

• A player always tries to win: if a player can place his own symbol (X or O) in a row which already contains two of his own symbols, he will do so.
• A player always tries to avoid that his opponent wins: if a player can place his own symbol (X or O) in a row which already contains two of the symbols of his opponent, he will do so.

Of course, the first rule has precedence over the second rule, because the game can be won in this way.

In the game shown on the right, 6 moves have been done. David plays with crosses (X) and Angela plays with circles (0). However, we don't know who started the game.

Yesterday evening, Helen and her husband invited their neighbours (two couples) for a dinner at home. The six of them sat at a round table. Helen tells you the following:

• "Victor sat on the left of the woman who sat on the left of the man who sat on the left of Anna.
• Esther sat on the left of the man who sat on the left of the woman who sat on the left of the man who sat on the left of the woman who sat on the left of my husband.
• Jim sat on the left of the woman who sat on the left of Roger.
• I did not sit beside my husband."

Jack and his wife went to a party where four other married couples were present. Every person shook hands with everyone he or she was not acquainted with. When the handshaking was over, Jack asked everyone, including his own wife, how many hands they shook. To his surprise, Jack got nine different answers.

A light bulb is hanging in a room. Outside of the room there are three switches, of which only one is connected to the lamp. In the starting situation, all switches are 'off' and the bulb is not lit.

Tom has three boxes with fruits in his barn: one box with apples, one box with pears, and one box with both apples and pears. The boxes have labels that describe the contents, but none of these labels is on the right box.

Assume that you have a number of long fuses, of which you only know that they burn for exactly one hour after you lighted them at one end. However, you don't know whether they burn with constant speed, so the first half of the fuse can be burnt in only ten minutes while the rest takes the other fifty minutes to burn completely. Also assume that you have a lighter.

At a family party, a grandfather, a grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law, and one daughter-in-law, sit at a table.

On the right you see a paper with a chessboard print on it. We want to cut the chessboard paper into pieces (over the lines!) such that each piece has twice as much squares of one color than of the other color (i.e. twice as much black squares as white squares or twice as much white squares as black squares).

On the right you see a small shunting-yard with two wagons (blue and green) and one locomotive (red). The wagons have a length of 5 meters, and the locomotive has a length of 10 meters. The dead end between the buffer-stop and the switch on the lower left has a a length of 5 meters (so the locomotive cannot change tracks on the lower left switch), and the dead end between the switch and the buffer-stop on the lower right has a a length of 15 meters. The locomotive can move forward and backward, and can both pull and push wagons.

Richard is a strange liar. He lies on six days of the week, but on the seventh day he always tells the truth. He made the following statements on three successive days:

Day 1: "I lie on Monday and Tuesday."
Day 2: "Today, it's Thursday, Saturday, or Sunday."
Day 3: "I lie on Wednesday and Friday."

Given are the following three equations:

1.  = 
2.  = 
3.  = 

Try to fill the total board (10x10-2) with bricks of size 2 ( and ), so no overlaps, no gaps, and no bricks crossing the borders.

A traveler, on his way to Eindhoven, reaches a road junction, where he can turn left or right. He knows that only one of the two roads leads to Eindhoven, but unfortunately, he does not know which one. Fortunately, he sees two twin-brothers standing at the road junction, and he decides to ask them for directions.

The traveler knows that one of the two brothers always tells the truth and the other one always lies. Unfortunately, he does not know which one always tells the truth and which one always lies.

Look at the figure below, which shows fifteen men. The figure is subdivided into three areas (upper left, upper right, and the bottom half).

By exchanging the upper two parts of the figure, one gets the figure below. This new figure however only shows fourteen men! (If you don't belief what happened here: please print it, cut it, and try it out yourself!)

Barbara has boxes in three sizes: large, standard, and small. She puts 11 large boxes on a table. She leaves some of these boxes empty, and in all the other boxes she puts 8 standard boxes. She leaves some of these standard boxes empty, and in all the other standard boxes she puts 8 (empty) small boxes. Now, 102 of all the boxes on the table are empty.

There are three Federation Officers assigned to take three hostile aliens to "Peace Talks" on another planet. However, they must follow the following rules:

• They have only one small space ship.
• Only two individuals can ride in the space ship each time.
• All Federation Officers can pilot the space ship, but only one alien can pilot the ship.
• If at any time there are both Federation Officers and aliens on a planet, then there must always be more (or the same number of) Federation Officers than aliens on that planet. This is because if there are more aliens than Federation Officers, then the aliens will kill the Federation Officers. Count any individual in the space ship when it is on one planet as being on that planet.
• The one space ship is the only means of transportation. There is no other way to get to the "Peace Talks". No one can exit the space ship while it is in flight.
• To start off, all the Federation Officers and aliens are on the same planet.

The gentlemen Dutch, English, Painter, and Writer are all teachers at the same secondary school. Each teacher teaches two different subjects. Furthermore:

• Three teachers teach Dutch language
• There is only one math teacher
• There are two teachers for chemistry
• Two teachers, Simon and mister English, teach history
• Peter doesn't teach Dutch language
• Steven is chemistry teacher
• Mister Dutch doesn't teach any course that is tought by Karl or mister Painter.