Three-piece burrs

For the simplest of all burrs, there exists no regular solution. The first part will show why. The second part will show how people have overcome the problem by relaxing some of the constraints to construct non-regular three-piece burrs.

Regular three-piece burrs

For regular three piece burrs we are looking at rods of the size 2*2*6. We use the more common length of 6 in preference over the minimal size 4. Since the core of a three piece burr is 8 (Lemma 4.1.1), there are potentially 2⁸=256 possible rods. By excluding disjoint and duplicate rods there are exactly 28 unique ones, of which 9 are notchable. A list of all the pieces can be found on the Three-piece burr pieces page.

Not all of those rods could actually be used in the construction of a regular three-piece burr.

Non-regular three-piece burrs

While there are no regular three piece burrs, there are, however, a few solutions to a non-regular three-piece burr. Some of these designs are described in the following sections.

Segerblom's three-piece burr

In April 1899, Scientific American published a puzzle, designed by Wilhelm Segerblom of Wakefield, Massachusetts. This design is also described in "Puzzles Old & New", p.66 [Slocum86], and in the "Book of Ingenious & Diabolical Puzzles", p. 73 [Slocum94]. All three pieces are identical. There exists only one solution since the pieces and their mirror images are identical. To assemble, all three pieces have to be slid together in a diagonal movement. It is not possible to put two pieces together and then slide the third one in.

Improved Segerblom three-piece burr

The "Book of Ingenious & Diabolical Puzzles" mentions an improved version of the Segerblom design [Slocum94]. The picture in the book is too unclear to give an exact design. However, it looks as if the improvement consist in the addition of a triangular section to improve stability, but without filling the center completely. My best guess is a design as shown in the figure to the right.

Wyatt's three-piece burr

Edwin Wyatt, describes in his booklet "Puzzles in Wood" a version which requires a piece which can be rotated to make room to slide the other two pieces together [Wyatt28]. This design relaxes the constraint that rods can only have notches in multiples of 1*1*1 cubes. One of the rods has a notch leaving only a cylindrical part around which the piece can be rotated. Since piece #3 has a mirror image of itself, there are two possible solutions to this design. They are mirror images of each other.

Nob Yashigahara's fake three-piece burr

Nob Yashigahara invented this three-piece burr which is made up of only two pieces! [Slocum94, p.72]. The design relaxes the constraint of square rods by taking two rods of size 2*4*6 and cutting them as shown in the following figure.
	If you make the two rods from three kinds of woods, it will be hard to tell that this is not a three-piece burr, but just looks like one.