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I recently made a trip to the pick-a-brick at the Orlando LEGO Imagination
Center and spent time stacking bricks to fit inside the large cup. After I
returned home and counted my booty (1071.67 cubic bricks) I decided to
investigate what the maximum amount that the cup would hold was.
It didn't take much thought to see that a solid block leaves the least wasted
space. In this case, the block is the shape of a truncated cone, whose upper
and lower diameter match that of the top and bottom of the cup.
A quick check of the cup against my circle templates and some construction
yielded the 2 diameters that fit nicely in the cup.
I started construction of the cone in the middle at an intermediate diameter
of 9 studs, building 2 interlocking layers. This provided a stable platform
from which to do further construction.
The plan was to build the central cylinder from any arrangement of
homogeneous stacks of bricks to reach the bottom of the cup. After that was
completed, homogeneous stacks of 1xn bricks would be added as needed outside the
central cylinder to fill out to the edge of the cup at the various heights.
With the small end of the cup filled, bricks were readily stacked in a similar
manner to fill the large end of the cup.
The resulting cone is 15 bricks high, and thanks to the interlocking layer,
it can easily be picked up without falling apart.
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How to build the cone:
The resulting cone has 6 distinct layers.
The top 3 layers contain the central cylinder mentioned above, which is a 7x7
square, 9 bricks high. Centered on each side is a 1x5 area 6 bricks high,
topped by a 1x3 area 3 bricks high. Centered outside the 1x5 area is a 1x1 area
2 bricks high.
So, the top layer has a surface of 61 studs (3 bricks high), the second layer
a surface of 69 studs (4 bricks high) , and the third layer a surface of 73
studs (2 bricks high).
The fourth layer is the interlocking stable platform. It is a 7x7 square
with a 1x7 area and a 1x3 area centered on each side, giving it a surface area
of 89 studs (3 bricks high).
The fifth layer is the 7x7 square with a 1x7 and 1x5 area centered on each
side, giving it a surface area of 97 studs (2 bricks high).
The sixth layer is a 9x9 square with a 1x5 area centered on each side, giving
it a surface area of 101 studs (1 brick high).
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The resulting cone contains 1167 cubic bricks, and is inserted into the cup
studs down.
There are, however, four more opportunities to add to the total that the cup
will hold.
The first is in the groove at the bottom of the cup, which holds a total of
36 1x1's, or 18 1x2's. (Add 36 more cubic bricks.)
The second is in the lid stud, which holds the equivelent of 4 2x4's, and 6
1x1's.. (Add 38 more cubic bricks.)
The third is in the gaps between the four edges of the cone and the sides of
layer two, which fit 4 more 2x4 plates. (Add 10 & 2/3 more cubic bricks.)
Putting these in place requires a small piece of tape to hold each in place
while inserting the assembly into the cup.
The fourth is a layer of plates on the large end of the cone, which can hold
11 2x4 plates. Note that packing geometry does not allow these 11 plates to
cover the entire end of the cone. Some space is neccessarily wasted for want of
2x2 or 1xn plates. (Add 29 & 1/3 more cubic bricks.)
This brings the total to 1281 cubic bricks. If you want a "hard lock" on the
lid, remove the layer of 11 2x4 plates and the 6 1x1's in the lid stud. This
reduces the total to 1245 & 2/3 cb.
The above maximizes the brick volume (1241 cb.) and fills in the rest with
plates (40 cb.) If you are willing to sacrifice some bricks for plates the
total volume can be improved upon further!!
The strategy is to build a central 7x7 block 13 bricks high of any desired
contents. It is helpful if it holds together as one solid block. Now, instead
of filling in the gaps with bricks, the bulk of it will be filled with plates
shaped to fit the 4 curved sides. 38 2x4 plates are used to build on a trapaziod
footprint (13 studs long, base 8 studs wide, apex 4 studs wide) with a curved
top that approximates the curve of the side of the cup. At the center of the
base it will be 5 plates thick and taper down to 1 plate thick at the apex. (I
havn't taken a picture of it so, "The details are left as an exercise for the
student." It does hold together as one solid unit, and, if desired, three
stacks of 3 2x4 plates can each be replaced by a 2x4 brick.)
The bottom groove of the cup is filled as before, followed by the central
block (studs down) and the 4 plate constructions nestled centered on each side.
With these pushed down in as far as they will go there is some room at each of
the four corners to put a 7 high and 3 high stack of 1x1 bricks. Along the top
of each plate construction is room for a 4 high stack of 1x2's. Across the
bottom of the central block is room for 8 2x4 plates. The lid is also filled as
before. Hold the lid on tight until it is taped on.
The grand total of this packing is 1315 & 2/3 cb.!! The volume break down by
bricks/plates is: brick volume = 889 cb., plate volume = 426 & 2/3 cb. If you
want a "hard lock" on the lid you'll have to leave out the layer of 8 2x4
plates, the 6 1x1's in the lid stud, and the 3 high stack of 1x1's at each
corner. This reduces the total to 1276 & 1/3 cb.
Brian H. Nielsen
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Message has 3 Replies:
 | | Re: Improved Pick-A-Brick packing
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| Our biggest concern was to see how many 2x4 blocks we could easily get in each cup. So far the easiest way I have found is as below......... (URL) This results in 136-2x4, 1-2x2, 21-1x4, 18-1x2 plus room for a few other little items like tiles. This (...) (21 years ago, 12-Nov-03, to lugnet.general, lugnet.market.shopping)
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