MathDB

11

Part of 1990 Romania Team Selection Test

Problems(1)

m(n-k -1) = k(k -l -1), in a group of n persons,

Source: Romania IMO TST 1990 p11

2/19/2020
In a group of nn persons, (i) each person is acquainted to exactly kk others, (ii) any two acquainted persons have exactly ll common acquaintances, (iii) any two non-acquainted persons have exactly mm common acquaintances. Prove that m(n−k−1)=k(k−l−1)m(n-k -1) = k(k -l -1).
combinatorics