MathDB

All 16 members of F have exactly one element in common

Source:

September 15, 2010

combinatoricsSet systemsIntersectionIMO ShortlistIMO Longlist

Problem Statement

Let

K

denote the set

\{a, b, c, d, e\}

F

is a collection of

16

different subsets of

K

, and it is known that any three members of

F

have at least one element in common. Show that all

16

members of

F

have exactly one element in common.