6

Part of 2017 Federal Competition For Advanced Students, P2

Problems(1)

maximal n, exist n distinct subsets of {1,2,...,2017} that no 2 have it as union

Source: 48th Austrian Mathematical Olympiad National Competition (Final Round, part 2) 25th May 2017 p6

S = \{1,2,..., 2017\}

. Find the maximal

n

with the property that there exist

n

distinct subsets of

S

such that for no two subsets their union equals

S

.
Proposed by Gerhard Woeginger

SubsetsMaximalcombinatorics