Finding the minimum of $\frac pq + \frac rs$ for distinct integers $p, q, r, s$ from $\{1,2,3,4,5,\ldots,16,17\}$ Here is the question:

Four distinct integers $p$, $q$, $r$ and $s$ are chosen from the set $\{1, 2, 3, 4, 5, \ldots, 16, 17\}$. The minimum possible value of $\frac pq + \frac rs$ can be written as $\frac ab$, where $a$ and $b$ are positive, co-prime integers. What is the value of $a+b$?

I got the answer as $321$. I took the numbers as $\frac pq$ as $\frac 1{16}$ and $\frac rs$ as $\frac 2{17}$ and added them to get $\frac ab = \frac{49}{272}$. Well I first took $\frac pq$ and $\frac rs$ as $\frac 1{17}$ and $\frac 2{16}$ respectively.
So without calculating both the results I wouldn't have got the answer. So can you help me by giving the way to get the answer?

$\frac{1}{16} + \frac{2}{17} = \frac{1}{16} + \frac{1}{17} + \frac{1}{17}$
$\frac{2}{16} + \frac{1}{17} = \frac{1}{16} + \frac{1}{16} + \frac{1}{17}$
So obviously the first one is smaller.
