Think before choose

$\begin{aligned} S & = \frac {16}{17} + \frac {17}{18} + \frac {18}{19} + \cdots + \frac {32}{33} \\ & = \frac {17-1}{17} + \frac {18-1}{18} + \frac {19-1}{19} + \cdots + \frac {33-1}{33} \\ & = 17 - \color{#3D99F6} \left(\frac {1}{17} + \frac {1}{18} + \frac {1}{19} + \cdots + \frac {1}{33} \right) \\ & \ {\color{#D61F06}>} \ 17 - \color{#3D99F6} \left(\frac {1}{17} + \frac {1}{17} + \frac {1}{17} + \cdots + \frac {1}{17} \right) \\ & > 17 - {\color{#3D99F6} 1} = 16 \end{aligned}$

$\implies S \ \boxed{>} \ 16$

There are seventeen terms here. The first one is equal to $16/17$ ; the other ones are all greater.

(Consider, e.g. that $\frac{17}{18} = 1 - \frac1{18} > 1 - \frac1{17} = \frac{16}{17}$ .)

Thus we have $\frac{16}{17} + \frac{17}{18} + \cdots + \frac{32}{33} \boxed{>} \underbrace{\frac{16}{17} + \frac{16}{17} + \cdots}_{17\times} = 17\cdot \frac{16}{17} = 16.$