Archive for December 2008

Chasing the terrorist

December 4, 2008

(Presented by Wojciech Mostowski in IPA herfstdagen 08)

There are two characters that move along a line: a terrorist and a policeman. The line has only discrete positions, this is, it is possible to count the possible positions on the line. However there are infinitely many positions to both sides of the line.

The terrorist is very predictable. At each move, he advances one position on the line. The initial position and direction is unknown, but he never changes the direction.

The policeman can jump between any position in the line, but he can only move at the same time the terrorist moves.

The question is: is there any strategy  for the policeman to move along the line that guarantees that he will catch the terrorist in a finite number of steps? Catching the terrorist means being on the same position as him.

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Cube of cheese

December 4, 2008

(Presented by Wojciech Mostowski in IPA herfstdagen 08)

Given a cheese cube the goal is to cut it into exactly 27 equal and smaller cubes.

The question is: what is the minimum number of cuts you need to make, and why? Take into account that you can move the pieces of cheese between each cut.

Half cube

December 4, 2008

(Presented by Arnar Birgisson in IPA herfstdagen 08)

You have a cube and you attach a string to one of its corners. You then pull the string up, and the gravity makes the cube stay with one corner up, and the opposite corner exactly under the upper corner.

You now grab a knife and cut the cube horizontally, exactly on the middle height.

The question is simple: what is the 2D shape you see on the part of the cube that has been cut?

(The answer is not difficult to get, but it is a bit unintuitive.)