2015 groups of 5 distinct numbers, for any 2 groups exactly 4 no occur in both
Source: Dutch NMO 2015 p1
September 7, 2019
combinatoricsSetsmaximum
Problem Statement
We make groups of numbers. Each group consists of fi ve distinct numbers. A number may occur in multiple groups. For any two groups, there are exactly four numbers that occur in both groups.
(a) Determine whether it is possible to make groups.
(b) If all groups together must contain exactly six distinct numbers, what is the greatest number of groups that you can make?
(c) If all groups together must contain exactly seven distinct numbers, what is the greatest number of groups that you can make?