Figure 1: A Standard Lego brick, measuring 8 mm square (1LC in this article’s measurements), with a standard U.S. quarter
and Darth Vader for size comparison.
Figure 2: Lego promotional brickbox
(left) and for-purchase brickbox cup
(right). Which holds more?
to simulate. It is possible, for small
problems, to simulate the system itself, which entails actual Legos, actual
children and an actual box. And here’s
where I stopped being in control and
the problem took over.
I went to the store and purchased a
(non-promotional) Lego brickbox. This
one is different than the promotional version, because it is a large round cup, and
now things get really interesting. Because
while packing square Legos in a square
box is easy, packing square Legos in a
round cup is hard. My idea was to have
a set of Lego bricks, 1x1, 1x4, 2x2 and
2x4 of different colors for a group of children to toss into the promotional (square)
box. We could then determine what an
“average” random fill of bricks might be.
I didn’t concern myself too much with
optimally packing the cup; I reasoned that
it was so much larger than the box (946
vs. 670 cubic centimeters) that I wouldn’t
need to worry too much about optimizing.
Naïvely, based solely on volume, one
might estimate that the large cup holds
1,678 bricks. This is a naïve measure because it simply divides the volume of the
box by the volume of the bricks.
I turned out to be dead wrong;
my brick purchase that haphazardly
filled the cup only filled the box (when
optimally stacked) a little more than
half way! This is because it’s difficult
to pack squares into a round container,
even more so when you don’t try.
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