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Math + Woodwork = Homemade Wooden Burr Puzzles

10 August 2008 5 Comments

This weekend I was in dire need of a mental escape. Woodworking in the basement is both a physical and mental endeavour which generally only succeeds when you give it adequate focus. I don’t recommend woodworking when you’re mind’s not on your work [LINK].

I came across IBM’s website on burr puzzles [LINK] and decided to make one.

"Burr puzzles are interlocking puzzles known in Europe and Asia since at least the 18th century. Traditionally they are made from wood….and require special wood so that the pieces do not change shape too much in changing temperature and humidity."

"From the late 1980s to the mid 1990 Bill Cutler and others undertook a complete analysis of all six-piece burrs…. From this analysis we now know that there are roughly 35.65 billion ways to assemble burr puzzles pieces (71.3 billion if mirror images are counted also). Of these 35.65 billion logical assemblies 5.95 billion can be taken apart."

Burrs? You had me at "35.65 billion".

Winkler pieces I first picked "David Winkler’s favorite level 5 burr" [LINK]. This is a "notchable" burr meaning you can construct it entirely by notching the pieces. I used a bit of red-oak I had laying around. This burr is 6 units long, 2 wide. The unit size in my case is 3/8" which I found a good size. The design in this case is a "5.4" meaning there are 5 moves required to remove the first piece, then 4 to remove the 2nd.

My kids got a good kick out of this one and they’ll likely play with it in years to come. Sunday night I caught the bug again and decided to make another. This time a "general" design meaning one where the pieces are not just notched but also have some partial voids. Slightly more complex to create but allows for more complex solution. I decided to go all out and chose Peter Marineau’s
Piston Puzzle Burr [LINK].

"1986: Peter Marineau designed this puzzle by hand. It was the highest level burr known before Bill Cutler did his exhaustive computer analysis."

I made this one out of cherry with its tighter grain and the fit is a lot better, mostly due to me taking my time. The action in Marineau’s is such that the first piece only comes out after a full 9 moves then 3 more for the 2nd piece. So cool.

I imagine this is the type of puzzle my grandfather would have enjoyed making if he had had the same resources available as me. The chisel remains the most dangerous tool in my shop.


  • TERESA said:


  • Francis said:

    Thanks Teresa, the thumb is ok. Still numb. I nicked it a few times with the chisel but couldn’t feel it. I hit the same thumb with a hammer two weeks back and felt that big time so I think the feeling will eventually come back 😉

  • myron said:

    where do I go once on the ibm link? initially it apologizes for the page I requested was unable to display…

  • Francis (author) said:

    Looks like IBM took this site down, (this was a while ago). Try googling for Wooden Burr Patterns, you’ll find a bunch.

  • Jack said:

    It’s still possible to see much of the original site on the wayback machine. However, since I don’t have Java installed, I don’t know if any of the applets work.

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