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Rectangle containing exactly one point

Source: RMM 2015 Problem 6

March 1, 2015

RMMrectanglecombinatorial geometrycombinatoricsRMM 2015

Problem Statement

Given a positive integer

T

, determine the largest real number

U

satisfying the following condition: for every set

C

of

4n

points in the interior of the unit square

U

, there exists a rectangle

T

contained in

U

such that

\bullet

the sides of

T

are parallel to the sides of

U

;

\bullet

the interior of

T

contains exactly one point of

C

;

\bullet

the area of

T

is at least

\mu

.

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