MathDB

We are given

1988

unit cubes. Using some or all of these cubes, we form three quadratic boards

A, B,C

of dimensions

a \times a \times 1

b \times b \times 1

, and

c \times c \times 1

respectively, where

a \le b \le c

. Now we place board

B

on board

C

so that each cube of

B

is precisely above a cube of

C

and

B

does not overlap

C

. Similarly, we place

A

B

. This gives us a three-floor tower. What choice of

a, b

and

c

gives the maximum number of such three-floor towers?

8