NL-NWO 2015 Problem 1
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?
Dataset text AI-MO AoPS. Quoted with source.
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