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M2805
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(1)
Combinatorics with set and arithmetic means
Source: Caucasus MO 2024, Seniors P7
3/13/2024
Find the largest positive integer
n
n
n
, such that there exists a finite set
A
A
A
of
n
n
n
reals, such that for any two distinct elements of
A
A
A
, there exists another element from
A
A
A
, so that the arithmetic mean of two of these three elements equals the third one.
combinatorics