ISL 1990 Problem 33

Let S be a 1990-element set and P be a set of 100-ary sequences $(a_1,a_2,...,a_{100})$ ,where $a_i's$ are distinct elements of S.An ordered pair (x,y) of elements of S is said to appear in $(a_1,a_2,...,a_{100})$ if $x=a_i$ and $y=a_j$ for some i,j with $1\leq i<j\leq 100$ .Assume that every ordered pair (x,y) of elements of S appears in at most one member in P.Show that $|P|\leq 800$ .