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.

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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?