Relationship between DFT input sequence and magnitude
In general, one can't infer the magnitude of the DFT coefficients from the values of the input sequence if by inference one means a process that is much more amenable to manual computing than just evaluating the DFT directly. In a sense, you are asking for "half" (or more) of the information that the DFT provides without doing much work for it; TANSTAAFL. What can be done easily is to get a (weak) upper bound (in some sense, a trivial upper bound) on $|X[k]|$. We have that
\begin{align}
|X[k]| &amp;= \left|\sum_{n=0}^{N-1} x[n]\exp(-j2\pi kn/N)\right|\\
&amp;\leq \sum_{n=0}^{N-1} \left|x[n]\exp(-j2\pi kn/N)\right|\\
&amp;\leq \sum_{n=0}^{N-1} \left|x[n]\right|\\
&amp;\leq N \max_n |x[n]|.
\end{align}
In typical cases of DFT computations, this is a very weak bound. In the 
OP's special case however, one can use the fact that $16$ of the $32$ $x[n]$ are $0$ (and the rest have value $1$) to tweak the bound to 
$$|X[k]| \leq 16.$$
Since jomegaaA's calculations show that $X[0]$ does indeed have value $16$ in this instance, no tighter bound can be found in this particular instance.