CMO 1999 Problem 4

Suppose $a_1,a_2,\cdots,a_8$ are eight distinct integers from $\{1,2,\cdots,16,17\}$ . Show that there is an integer $k > 0$ such that the equation $a_i - a_j = k$ has at least three different solutions. Also, find a specific set of 7 distinct integers from $\{1,2,\ldots,16,17\}$ such that the equation $a_i - a_j = k$ does not have three distinct solutions for any $k > 0$ .