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International Contests
Austrian-Polish
1995 Austrian-Polish Competition
2
2
Part of
1995 Austrian-Polish Competition
Problems
(1)
subset Y of X with property that there is no disk K such that K\cap X = Y
Source: Austrian - Polish 1995 APMC
5/3/2020
Let
X
=
{
A
1
,
A
2
,
A
3
,
A
4
}
X= \{A_1, A_2, A_3, A_4\}
X
=
{
A
1
,
A
2
,
A
3
,
A
4
}
be a set of four distinct points in the plane. Show that there exists a subset
Y
Y
Y
of
X
X
X
with the property that there is no (closed) disk
K
K
K
such that
K
∩
X
=
Y
K\cap X = Y
K
∩
X
=
Y
.
Subsets
set
combinatorial geometry
combinatorics
disks