Two politicians go to a bar and order two glasses of vodka on the rocks. The first politician quickly empties his glass, then orders a second one, a third one… The second politician patiently drinks his own vodka, but about 20 minutes later, he drops down dead. The police discovered that the barman tried to assassinate both politicians, but how come the second one died and the first one lived?
SOLUTION
The poison was in the ice cubes, so the second politician drank them when they melted in his drink.
A man is found in a room without any windows, with just one door which is locked from the inside. The man is hanging from a ceiling fan, dead, 4 feet above the floor. The room is completely empty, except for the man, the fan, and a puddle of water on the floor. How did the man die?
SOLUTION
The man used a block of ice so that he could hang himself, and then the ice melted into the puddle of water.
Imagine the following game occurs on a cylindrical board, on which the a-file and h-file are attached to each other. White plays first and mates Black in 2 moves.
SOLUTION
White plays Rook on a5, then Ra1#. He can’t take the pawn on a6, because Black will take back with the pawn on h7.
You have a glass with perfectly cylindrical shape which has some water in it. How can you figure out if the glass is exactly half full without using any measurement tools (like a ruler)?
SOLUTION
Use the geometry of the cylinder. Start tilting the glass until the water surface gets either to the top or the bottom edge. If the glass is exactly half full, then the surface should touch both edges simultaneously.
A town consists of 3 horizontal and 3 vertical roads, separated by 4 square blocks. A policeman and a thief are running along the roads with speeds of 21km/h and 10km/h respectively. Show that the policeman has a strategy ensuring he will eventually see the thief.
Remark: The policeman can see the thief if they are on the same road at some moment. He has no idea about his position at any time.
SOLUTION
A working strategy for the policeman would be to go to the center and to start encompassing the four blocks clock-wise one by one, in a clockwise manner.
Since the policeman is twice as fast as the thief if the thief is in the center of the town at some point, then there exists a moment in which the policeman is in the center, and the thief is not on the boundary, i.e. he gets shot.
Now, assuming the thief never visits the center, his angle with respect to the coordinate system defined by the two middle roads changes continuously. The angle of the policeman with respect to the same coordinate system can be defined to change continuously as well. Since the policeman needs less time to increase his angle with 360 degrees than the thief, there will be a moment when the two have the same angle. However, this implies that the policeman will be able to see the thief and shoot him.
