MathDB

Let

n>1

be an integer. Hippo chooses a list of

n

points in the plane

P_1, \dots, P_n

; some of these points may coincide, but not all of them can be identical. After this, Wombat picks a point from the list

X

and measures the distances from it to the other

n-1

points in the list. The average of the resulting

n-1

numbers will be denoted

m(X)

. Find all values of

n

for which Hippo can prepare the list in such a way, that for any point

X

Wombat may pick, he can point to a point

Y

from the list such that

XY=m(X)

Problem Statement