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Kürschák Math Competition
2019 Kurschak Competition
2
2
Part of
2019 Kurschak Competition
Problems
(1)
Family of sets with a regular property
Source: Kürschák competition 2019 P2
2/17/2020
Find all family
F
\mathcal{F}
F
of subsets of
[
n
]
[n]
[
n
]
such that for any nonempty subset
X
⊆
[
n
]
X\subseteq [n]
X
⊆
[
n
]
, exactly half of the elements
A
∈
F
A\in \mathcal{F}
A
∈
F
satisfies that
∣
A
∩
X
∣
|A\cap X|
∣
A
∩
X
∣
is even.
combinatorics