## Task 4 - 060924

The students Brigitte, Christina, Dorothea, Eva, Inge, and Monika and the students Anton, Fred, Günter, Helmut, Jürgen, and Kurt of a drama group want to perform a dance. The dance will be performed in pairs.

1) In no pair should the male partner be shorter than the female partner.

In addition, some participants have various wishes:

2) Christina does not want to dance with Anton, who is shorter than Brigitte.
3) Jürgen only wants to dance with Dorothea or Monika.
4) Fred, who is taller than Helmut but shorter than Anton, only wants to dance with Eva or Monika.
5) Kurt, who knows that Eva is taller than Anton, tries to find an arrangement that meets all the wishes.

List all possible pairings of these students for the dance that satisfy the given conditions (1) to (5)!

The task is to be understood in such a way that all possible pairings of the students for the dance should be given, which, based on the information provided, cannot be ruled out as incompatible with one or more of the conditions (1) to (5).
From Fred $<$ Anton, and Anton $<$ Eva, it follows that Fred $<$ Eva. This leads to the pair Fred with Monika, and Jürgen with Dorothea. From Anton $<$ Brigitte and Anton $<$ Eva, it follows that Christina does not form a pair with Anton, i.e., Anton with Inge.

From Helmut $<$ Anton $<$ Eva and Helmut $<$ Anton $<$ Brigitte, Helmut forms a pair with Christina. There remain exactly two possibilities for Günter, Kurt, and Brigitte, Eva, namely the following:

1. Fred and Monika, Jürgen and Dorothea, Anton and Inge, Helmut and Christina, Günter and Brigitte, Kurt and Eva.
2. Fred and Monika, Jürgen and Dorothea, Anton and Inge, Helmut and Christina, Günter and Eva, Kurt and Brigitte.