MathDB

Determine all integers

n \geq 3

for which there exists a conguration of

n

points in the plane, no three collinear, that can be labelled

1

through

n

in two different ways, so that the following condition be satisfied: For every triple

(i,j,k), 1 \leq i < j < k \leq n

, the triangle

ijk

in one labelling has the same orientation as the triangle labelled

ijk

in the other, except for

(i,j,k) = (1,2,3)

Problem Statement