Duplo Challenge

Small children (and their parents) sometimes struggle with the small size of Lego elements. The Lego company therefore introduced (at least 20 years ago) the "Duplo", a line of oversized Lego elements.

Most Lego (and therefore Duplo) constructions are generally rectilinear, reflecting the basic shape and obvious connectivity of the elements from which they are constructed.

The DuploChallenge is to construct an approximately cylindrical tower, surrounding an open center, from interlocking Duplo blocks and/or bricks. A square Duplo Block and brick look something like the following (from the top):

Square

               +------+
               | O  O |
               |      |
               | O  O |
               +------+

Brick

               +------------+
               | O  O  O  O |
               |            |
               | O  O  O  O |
               +------------+

In most Duplo sets, the squares come in single- and double-height varieties.

Hint: You'll want at least 30 or so blocks to build an interestingly tall tower.

I'll happily provide a picture of the result of anyone would like. Successful solutions can be built from a variety of combinations, and demonstrate surprising variety in size, appearance, and proportion.

By the way, there are important lessons about modularity, EmergentBehavior, and emergent properties of simple systems to be learned from the exercise.

-- TomStambaugh

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Is it legal to melt the blocks first?

Well, it might be legal, but your children will never forgive you. No, this is a completely non-destructive exercise.

I wouldn't destroy the blocks, just change their shape.

You must be one of those software-types. Changing the shape of the blocks will disqualify your entry.

OK, can I mortar them with PlayDoh??

Sounds like you're stumped, and therefore perhaps eager to participate in one of my obscenely expensive workshops on the topic.

I'm not eager to participate in anything that's obscenely expensive. I've made lego forms that were close to cylinders, but I doubt a true cylinder can be made without deforming the bricks or suspending them in another media. How strict is your definition of cylinder? Is a square a cylinder? An octagon? Etc?

I mean a closed shape with more than four sides, whose interior angles are equal to each other and each greater than ninety degrees. A pentagon, hexagon, septagon, octagon, etc., will do fine. That's why I said approximately cylindrical.

Do the sides have to be filled or can there be gaps?

Gaps are ok, it's the overall shape (looking down from the top) that matters.

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I'd build it from stacked rings of bricks; each ring would consist of 4x2 bricks (long axes tangential to the ring) with roughly brick-sized spaces in between, and the rings would be lined up so bricks were over spaces and vice-versa. The connection between successive rings of bricks would be at the innermost end bumps, which i denote with an X:

               +------------+
               | O  O  O  O |
               |            |
               | X  O  O  X |
               +------------+
              (inside of ring)

These bumps fit into the sockets in the same positions in the ring above, except that due to the out-of-phase apposition of the rings, the bumps on a given block fit into holes in two different blocks.

The curve angle is constrained by the fact that the 'skirt' of the upper brick cannot run through a bump. I can't say what angles are permissible, although 90 degrees is; it leads to a structure like this (only two layers are shown):

 lower layer:

               +------------+
               | O  O  O  O |
               |            |
               | X  O  O  X |
               +------------+


               +------------+
               | X  O  O  X |
               |            |
               | O  O  O  O |
               +------------+

 upper layer:

            +------+    +------+
            | O  X |    | X  O |
            |      |    |      |
            |      |    |      |
            | O  O |    | O  O |
            |      |    |      |
            |      |    |      |
            | O  O |    | O  O |
            |      |    |      |
            |      |    |      |
            | O  X |    | X  O |
            +------+    +------+

That would look a lot better in a square font.

-- TomAnderson

Bingo, that's pretty much the approach. It turns out that the little square ones work well. Once the curvy-trick is understood, you can build squarish modules and therefore vary the "texture" pretty much arbitrarily. I think it's a pretty good example of a property (flexibility) emerging from components that don't appear to offer it at first inspection.