In a shop, there were 4 dolls of different heights A, B, C and D. $D$ is neither as tall as $A$ nor as short as $C$. $B$ is shorter than $D$ but taller than $C$. If someone wants to purchase the tallest doll, which one should he/she purchase?

Let's map the height relations step-by-step:
1. "$D$ is neither as tall as $A$ nor as short as $C$ ": This means $D<A$ and $D>C$. So $A$ is taller than $D$.
2. "$B$ is shorter than $D$ but taller than $C$ ": This means $C<B<D$.

Combining both inequalities together:

$$C<B<D<A$$

Looking at the final chain, $A$ is clearly the tallest doll.