## Task 4 - 060614

In a house, exactly the following tenants live: Albrecht, Becker, Conrad, Dietrich, Ermler, Fritsche, Geißler, Hamann, Ilgner, Keies, Lorenz, Männig, Nolte, Oswald, Richter, and Pätzold.

On the ground floor and in each floor, exactly two tenants live, and the following is known:

Albrechts live two floors below Beckers.

Beckers live six floors above Conrads.

The Fritsche family lives next to the Geißler family.

The Männig family lives four floors above the Nolte family and two floors below the Fritsche family.

One floor above the Nolte family, the Oswald family lives.

The Albrecht family lives three floors above the Richter family, and the Pätzold family lives five floors below the Geißler family.

a) How many floors does the house have?

b) In which floor does the Albrecht family live?
The 16 tenants are represented by the initial letters of their names.

a) Since two families occupy each floor, the building has 7 floors in addition to the ground floor.

b) The following relationships apply:

$$
\begin{aligned}
a+2=b & (1) \quad ; \quad c+6=b \quad(2) \quad ; \quad f=g \quad(3) \quad ; \quad n+4=m \\
m+2=f & (5) \quad ; \quad n+1=o \quad(6) \quad ; \quad r+3=a \quad(7) \quad ; \quad p+5=g
\end{aligned}
$$

From (3) to (6), it follows that $n+6=o+5=m+2=f=g$. Since (8) also holds, Pätzold and Oswald must live on the same floor $(o=p)$.

Furthermore, from equations (1), (2), and (7), we get $c+6=r+5=a+2=b$. Therefore, $c$ and $n$ can only live on the ground floor or the 1st floor.

However, $c$ and $n$ cannot live on the same floor, as this would also make $r, o$, and $p$ immediate neighbors. If $n$ lives on the ground floor, then $o, p$, and $c$ would have to live on the 1st floor, which is not possible. Therefore, Nolte lives on the 1st floor, and Conrad lives on the ground floor, and Albrecht consequently lives on the 4th floor.