I've got to tell you what it was about this question that made me stop,
look it over, play with it, and try to answer it: It was the size of the piece
of land involved . . . 2¹⁵ square miles. I had a funny feeling about that piece
of land, so I went and looked it up, and sure enough, it was just as I suspected.
Let me put it this way:
-- South Carolina
-- West Virginia
-- Maryland
-- Hawaii
-- Massachusetts
-- Vermont
-- New Hampshire
-- New Jersey
-- Connecticut
-- Delaware
-- Rhode Island
Not one of these 11 states has that much land inside its borders.
-- Panama
-- Ireland
-- Costa Rica
-- Israel
-- Denmark
-- Netherlands
-- Switzerland
-- Taiwan
-- Belgium
-- Haiti
Not one of these 10 countries has that much land in it.
And ALL OF THESE PUT TOGETHER don't add up to that much land:
-- Fiji
-- Kuwait
-- Bahamas
-- Jamaica
-- Lebanon
-- Puerto Rico
But that's what the question says, so that's the way to work it.
It's only math.
=============================================
How many times does 8³ fit into 2¹⁵ ?
We need to evaluate 2¹⁵ / 8³ .
If the bases were the same, then we could simply subtract the exponents.
Notice that '8' is the same thing as 2³ .
So 8³ = (2³)³ = 2⁹ .
Now the big fraction can be written as 2¹⁵ / 2⁹ and that's 2⁶ .
And there you are.
If you start out with 2¹⁵ square miles of land, and start giving away pieces
of 8³ square miles (slightly more land than Hong Kong) to everyone who
walks by, then by the time only 2 million people have walked by, you'll have
nothing left.
But you'll have the last laugh ! Because you can't move a piece of land,
so all those people will have to live next to each other !
As for the second part of the question (Compute the actual number of pieces.),
I must confess that either it's a bogus question or else I just don't get it.
Since the dimensions of the original rectangle (roughly the same area as Belgium)
are not stated, and the pieces of 8³ square miles aren't even described as being
any particular shape, I don't really see any reason why the chopping up can't be
done in such a way that it results in exactly 2⁶ pieces.
In conclusion, I'll offer the wry observation that the only tiny number associated
with this problem is the 5 points.
