MathDB

We say that a rectangle with side lengths

a

and

b

fits inside a rectangle with side lengths

c

and

d

if either (

a \le c

and

b \le d

) or (

a \le d

and

b \le c

). For instance, a rectangle with side lengths

1

and

5

fits inside another rectangle with side lengths

1

and

5

, and also fits inside a rectangle with side lengths

6

and

2

. Suppose

S

is a set of

2019

rectangles, all with integer side lengths between

1

and

2018

inclusive. Show that there are three rectangles

A

B

, and

C

S

such that

A

fits inside

B

, and

B

fits inside

C

4