MathDB

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})

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

33