MathDB

Determine whether there exist two infinite point sequences

A_1,A_2,\ldots

and

B_1,B_2,\ldots

in the plane, such that for all

i,j,k

with

1\le i < j < k

, (i)

B_k

is on the line that passes through

A_i

and

A_j

if and only if

k=i+j

. (ii)

A_k

is on the line that passes through

B_i

and

B_j

if and only if

k=i+j

. (Proposed by Gerhard Woeginger, Austria)

Problem Statement