MathDB

Monica and Bogdan are playing a game, depending on given integers

n, k

. First, Monica writes some

k

positive numbers. Bogdan wins, if he is able to find

n

points on the plane with the following property: for any number

m

written by Monica, there are some two points chosen by Bogdan with distance exactly

m

between them. Otherwise, Monica wins.
Determine who has a winning strategy depending on

n, k

.
(Proposed by Fedir Yudin)

Problem Statement