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Vietnam Contests
Vietnam Team Selection Test
2023 Vietnam Team Selection Test
6
6
Part of
2023 Vietnam Team Selection Test
Problems
(1)
2-colorable way for numbers
Source: Vietnam TST 2023, P6
4/14/2023
Let
n
≥
3
n \ge 3
n
≥
3
be an integer and
S
S
S
be a set of
n
n
n
elements. Determine the largest integer
k
n
k_n
k
n
such that: for each selection of
k
n
k_n
k
n
3
−
3-
3
−
subsets of
S
S
S
, there exists a way to color elements of
S
S
S
with two colors such that none of the chosen
3
−
3-
3
−
subset is monochromatic.
combinatorics