In the first test, we can press the second button 3 times, then the balance will be equal to $2^3+2^3+2^3=24$.

In the second test, it can be shown that it is impossible to obtain a balance equal to $3$ using the given buttons.

In the third test, the following operations can be performed:

\begin{enumerate}
\item pressing the $2$ button, the balance is equal to $1$;
\item pressing the $2$ button, the balance is equal to $2$;
\item pressing the $2$ button, the balance is equal to $3$;
\item pressing the $1$ button, the balance is equal to $6$;
\item pressing the $1$ button, the balance is equal to $12$;
\item pressing the $2$ button, the balance is equal to $13$.
\end{enumerate}

It can be shown that these answers are minimal for each test.