MathDB

For every

n\geq 3

, determine all the configurations of

n

distinct points

X_1,X_2,\ldots,X_n

in the plane, with the property that for any pair of distinct points

X_i

X_j

there exists a permutation

\sigma

of the integers

\{1,\ldots,n\}

, such that

\textrm{d}(X_i,X_k) = \textrm{d}(X_j,X_{\sigma(k)})

for all

1\leq k \leq n

. (We write

\textrm{d}(X,Y)

to denote the distance between points

X

and

Y

.)
(United Kingdom) Luke Betts

Problem Statement