Johnny received a Jumbo Set of 1000 building blocks for his birthday.
He begins to assemble them into "bricks" of dimensions a x b x c
where of course a, b and c are integers, and a <= b<= c.
He notices that for each brick he builds, some of the blocks are
"outside" blocks [visible] and some are "inside" blocks [hidden
by the outside blocks.] He imagines that for some bricks the
numbers of outside and inside blocks must be equal; call such
a brick an Equal Brick.
With his set of blocks, how many different Equal Bricks can Johnny make?
Now for small bricks [a=1 or 2] there are no Inside Blocks.
And for larger bricks, the Inside Blocks will eventually dominate.
So there must be a finite number of Equal Bricks.
If Johnny wants to make all possible Equal Bricks, how many
Jumbo Sets of blocks will he need?