MathDB

Let

MNPQ

be a square of side length

1

, and

A , B , C , D

points on the sides

MN , NP , PQ

and

QM

respectively such that

AC \cdot BD=\frac{5}{4}

. Can the set

\{AB , BC , CD , DA \}

be partitioned into two subsets

S_1

and

S_2

of two elements each , so that each one has the sum of his elements a positive integer?

Problem Statement