FIVE- M IN U T E A N A LYST
Lego Brickbox
Computing the
distribution of random
bricks tossed into a box
is difficult, because each
layer is dependent on the
one below it. Also, real
children do things that
real children do, such as
shake the box to make the
Legos settle.
BY HARRISON
SCHRAMM, CAP
72
|
At the holidays, many children received special promotional “Brick Boxes” from Lego, which
may be taken back to the store and filled from the
brick repositories on the back wall in the store. After Christmas, one child, “Norah,” saw one of her
friends, “Tyler,” meticulously build a shape to fit
exactly in his box. She asked me, “How much better do you think that Tyler did by building an exact
shape than I did just by tossing what I wanted into
the box?” Like many things, this turned out to be a
much simpler question to ask than to answer! For
the remainder of the article, we will use the natural
unit of “Lego cubes” (LC), which are the size of a
1x1 Lego brick, as shown in Figure 1. So, a 2x4
brick has an area of 8LC, and so on.
First, an easy problem: The promotional brickbox is 11x11x9 LC, and has a capacity of 1,089
squares. Packing square bricks into a square box
is very easy. This turns out to be the only easy
thing about this problem.
Computing the distribution of random bricks
tossed into a box is difficult, because each layer is
dependent on the one below it. Also, real children
do things that real children do, such as shake the
box to make the Legos settle. A few minutes with
a paper and pencil convinced me that this was
not the proper approach. So, I decided to simulate. Now, computer simulation has some of the
same difficulties – imagine playing a 3-D version
of Tetris – but fortunately, this is not the only way
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