Archive for September 2008

Making a bigger square

September 16, 2008

(Presented at a dinner table in Marktoberdorf summer school 2008)

You start with four point in a plane, making a square. You can move any point A by:

  • Choosing another point B in the plane;
  • Mirror point A with respect to point B, jumping A over B.

The question is: can you arrive to a configuration where you have a bigger square formed by the points? If not, why not? Note that the final square can be rotated with respect to the original square.


Mixing water and milk

September 16, 2008

(Given by Stephanie, taken from a german website.)

A farmer has two pots, one is filled with milk, the other is filled with water. He decides to decrease the quality of the milk as follows:

  1. From pot 1 (containing only water in the beginning), he pours as many gallons into pot 2 (containing only milk in the beginning) that the contents of pot 2 are doubled.
  2. Then he pours from pot 2 back into pot 1 the same amount as has been water left in pot 1.
  3. Then again he pours from pot 1 as many gallons into pot 2 that the contents of pot 2 double.

In this way, in the end both pots contained the same amount of liquid, just that pot 2 contains 2 gallons more water than milk.

Question: How many gallons of water and milk had the farmer in the beginning?