MathDB
Problems
Contests
International Contests
Austrian-Polish
1999 Austrian-Polish Competition
1
1
Part of
1999 Austrian-Polish Competition
Problems
(1)
each element of M belongs to 0, 3, or 6 of the subsets $A_1,...,A_6
Source: Austrian - Polish 1999 APMC
5/4/2020
Find the number of
6
6
6
-tuples
(
A
1
,
A
2
,
.
.
.
,
A
6
)
(A_1,A_2,...,A_6)
(
A
1
,
A
2
,
...
,
A
6
)
of subsets of
M
=
{
1
,
.
.
.
,
n
}
M = \{1,..., n\}
M
=
{
1
,
...
,
n
}
(not necessarily different) such that each element of
M
M
M
belongs to zero, three, or six of the subsets
A
1
,
.
.
.
,
A
6
A_1,...,A_6
A
1
,
...
,
A
6
.
Subsets
combinatorics