\section*{Task 1 - 041021}

Four people have the first names Arnold, Bernhard, Conrad, and Dietrich. The last names of these people are also Arnold, Bernhard, Conrad, and Dietrich.

Furthermore, we know the following:

a) None of the four people have the same first and last name.

b) Conrad does not have the last name Arnold.

c) Bernhard's last name matches the first name of the person whose last name matches the first name of the person who has the last name Dietrich.

What are the first and last names of each of the four people?
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The four people are denoted by the initials of their first and last names. For unknown names, X, Y, and Z are used.

Then, due to c), the following people are: BX, XY, YD, DZ.

Due to a), \(\mathrm{X} \neq \mathrm{B}, \mathrm{Y} \neq \mathrm{D}\). Since each name appears exactly once as a first or last name, and thus \(\mathrm{Y} \neq \mathrm{B}, \mathrm{X} \neq \mathrm{D}\), it follows from b) that only \(\mathrm{X}=\mathrm{A}, \mathrm{Y}=\mathrm{C}, \mathrm{Z}=\mathrm{B}\) is possible.

The four people are: Arnold Conrad, Bernhard Arnold, Conrad Dietrich, and Dietrich Bernhard.