MathDB

For

i = 1,2, \ldots, 1991

, we choose

n_i

points and write number

i

on them (each point has only written one number on it). A set of chords are drawn such that:
(i) They are pairwise non-intersecting. (ii) The endpoints of each chord have distinct numbers.
If for all possible assignments of numbers the operation can always be done, find the necessary and sufficient condition the numbers

n_1, n_2, \ldots, n_{1991}

must satisfy for this to be possible.

Problem Statement