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Turkey Contests
Turkey Team Selection Test
2023 Turkey Team Selection Test
4
4
Part of
2023 Turkey Team Selection Test
Problems
(1)
Set of sets with k elements find values of k
Source: 2023 Turkey TST D2 P4
3/29/2023
Let
k
k
k
be a positive integer and
S
S
S
be a set of sets which have
k
k
k
elements. For every
A
,
B
∈
S
A,B \in S
A
,
B
∈
S
and
A
≠
B
A\neq B
A
=
B
we have
A
Δ
B
∈
S
A \Delta B \in S
A
Δ
B
∈
S
. Find all values of
k
k
k
when
∣
S
∣
=
1023
|S|=1023
∣
S
∣
=
1023
and
∣
S
∣
=
2023
|S|=2023
∣
S
∣
=
2023
.Note:
A
Δ
B
=
(
A
∖
B
)
∪
(
B
∖
A
)
A \Delta B = (A \setminus B) \cup (B \setminus A)
A
Δ
B
=
(
A
∖
B
)
∪
(
B
∖
A
)
set theory
combinatorics