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Chile Contests
Chile National Olympiad
2018 Chile National Olympiad
5
5
Part of
2018 Chile National Olympiad
Problems
(1)
{1, 2, . . . , 20} has at least 2018 sumfree subsets
Source: 2018 Chile National Olympiad level 2 p5
10/22/2022
Consider the set
Ω
\Omega
Ω
formed by the first twenty natural numbers,
Ω
=
{
1
,
2
,
.
.
.
,
20
}
\Omega = \{1, 2, . . . , 20\}
Ω
=
{
1
,
2
,
...
,
20
}
. A nonempty subset
A
A
A
of
Ω
\Omega
Ω
is said to be sumfree [/i ] if for all pair of elements
x
,
y
∈
A
x, y \in A
x
,
y
∈
A
, the sum
(
x
+
y
)
(x + y)
(
x
+
y
)
is not in
A
A
A
, (
x
x
x
can be equal to
y
y
y
). Prove that
Ω
\Omega
Ω
has at least
2018
2018
2018
sumfree subsets.
combinatorics