MathDB

Let

n

points be given inside a rectangle

R

such that no two of them lie on a line parallel to one of the sides of

R

. The rectangle

R

is to be dissected into smaller rectangles with sides parallel to the sides of

R

in such a way that none of these rectangles contains any of the given points in its interior. Prove that we have to dissect

R

into at least

n + 1

smaller rectangles.
Proposed by Serbia

Problem Statement