MathDB

Let

n\geqslant 3

be a positive integer and

N=\{1,2,\ldots,n\}

and let

k>0

be a real number. Let's associate each non-empty of

N{}

with a point in the plane, such that any two distinct subsets correspond to different points. If the absolute value of the difference between the arithmetic means of the elements of two distinct non-empty subsets of

N{}

is at most

k{}

we connect the points associated with these subsets with a segment. Determine the minimum value of

k{}

such that the points associated with any two distinct non-empty subsets of

N{}

are connected by a segment or a broken line.
Cristi Săvescu

Problem Statement