Thursday, July 14, 2011

A flexible burr puzzle

(7 Feb 2013) I notice some debate about this post elsewhere online -- if you have questions feel free to leave a comment or contact me via the email address in my profile (right).

In 2002 George Miller devised an unusual puzzle titled Three Card Burr, made by laser cutting slots into three ordinary playing cards so they could be interlaced together. Interestingly, there's no practical way to disassemble the cards after the puzzle has been solved.

I was inspired by George Miller's Three Card Burr puzzle to create a more complex puzzle to exploit the SD300's ability to build sheet-like structures by creating a 3D model whose geometry can be mapped to the build material. I designed this flat model whose middle section is nominally 0.51mm thick, so it will be built using three thicknesses of 172-micron PVC sheet. The adjacent areas have two 0.34mm thick panels stacked one above the other and attached to the middle section by a 0.17mm thick strip to act as a hinge. The whole model is about 120mm x 70mm x 0.9 mm.

Here are my first 3 sample models, built in transparent material.

Like Three Card Burr assembling the puzzle begins by carefully interlacing the sheets together. It wasn't as difficult as I'd expected because the resiliency of the PVC material enabled me to flex the puzzle without tearing it.

Once the pieces are interlaced together, the hinged panels fold out and interlock at the corners to form a cube. This part was far more difficult than I'd expected because each corner depends upon its neighbors for stability, which meant each corner would come apart when I tried to assemble the next corner. I'd forgotten to allow for the thickness of the material in the corner dimensions, so the panels warped from excess tension.

Not bad for a first try, though. It proves the concept is basically sound; now I just have to adjust the dimensions and add something to make the corners more stable. Maybe a small tab or hook?


  1. Nice! I also got hold of one of the Three Card Burrs a little while ago, but I haven't ever assembled it because it cannot be disassembled again. I'm guessing a PVC version could be taken apart without tearing too.

  2. Three Card Burr really needs to be assembled to be fully appreciated. The finished puzzle is quite a stunning trophy, particularly as the cards are quite immobile.

    The one-way feature elegantly balances topology against the limitations of the cards' material properties. You must put the cards under a great deal of stress to assemble the puzzle, but the cards work together to keep that stress under control until you reach a fully-assembled equilibrium. Once it's assembled you can't go back because neighboring cards resist the movement instead of assisting it; the force required to overcome the resistance would exceed the material strength of the cards.

    A PVC version can be taken apart without tearing, but it takes more force than you might expect. But my cube puzzle is more elaborate than Three Card Burr, which puts more stress on the material, thereby pushing it close to its limit. It can be taken apart, but you could break the puzzle in doing so.