MathDB
Problems
Contests
National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
2004 Switzerland Team Selection Test
1
1
Part of
2004 Switzerland Team Selection Test
Problems
(1)
E(a)is the number of elements of $X_1\cup ... \cup X_n, \sum_{a\in S} E(a)
Source: Switzerland - Swiss TST 2004 p1
2/18/2020
Let
S
S
S
be the set of all n-tuples
(
X
1
,
.
.
.
,
X
n
)
(X_1,...,X_n)
(
X
1
,
...
,
X
n
)
of subsets of the set
{
1
,
2
,
.
.
,
1000
}
\{1,2,..,1000\}
{
1
,
2
,
..
,
1000
}
, not necessarily different and not necessarily nonempty. For
a
=
(
X
1
,
.
.
.
,
X
n
)
a = (X_1,...,X_n)
a
=
(
X
1
,
...
,
X
n
)
denote by
E
(
a
)
E(a)
E
(
a
)
the number of elements of
X
1
∪
.
.
.
∪
X
n
X_1\cup ... \cup X_n
X
1
∪
...
∪
X
n
. Find an explicit formula for the sum
∑
a
∈
S
E
(
a
)
\sum_{a\in S} E(a)
∑
a
∈
S
E
(
a
)
combinatorics
Sum
Subsets