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Problems
Contests
National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
2004 Switzerland Team Selection Test
9
9
Part of
2004 Switzerland Team Selection Test
Problems
(1)
subtraction of subsets
Source: Swiss 2004
10/11/2006
Let
A
1
,
.
.
.
,
A
n
A_{1}, ..., A_{n}
A
1
,
...
,
A
n
be different subsets of an
n
n
n
-element set
X
X
X
. Show that there exists
x
∈
X
x\in X
x
∈
X
such that the sets
A
1
−
{
x
}
,
A
2
−
{
x
}
,
.
.
.
,
A
n
−
{
x
}
A_{1}-\{x\}, A_{2}-\{x\}, ..., A_{n}-\{x\}
A
1
−
{
x
}
,
A
2
−
{
x
}
,
...
,
A
n
−
{
x
}
are all different.
induction
combinatorics unsolved
combinatorics