The Knights of the Round Table are gathering. Around the table are $34 $ chairs, numbered from 1 to $34$. When everyone has sat down, it turns out that between every two knights there is a maximum of $r$ places, which can be either empty or occupied by another knight. (a) For each $r \le 15$, determine the maximum number of knights present. (b) Determine for each $r \le 15$ how many sets of occupied seats there are that match meet the given and where the maximum number of knights is present.