Holey-6 Designers and their Designs BCPI logo billcutlerpuzzles.com

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Bill Cutler Puzzles, Inc. (Listed chronologically in order of my knowledge of their first design.)

Stewart Coffin, Lincoln, Massachusetts

Interrupted Slide - the first of Stewart's holey-6 designs. It is noteworthy for other reasons as well. With length 6 pieces, is has nine assemblies and two solutions, both of level-3. With length eight pieces, there are still, of course, nine assemblies, but only one of the solutions remains. Computer output with both lengths is included.

Triple Slide - a design with a unique level-3 solution in which all of the splits are three pieces one way and three the other. The length of the pieces can be eight or longer. I have since seen many similar designs.

Coffin's Improved Burr - the first move is level-2, but the second piece is level-3 to remove. The computer output shows the subassembly analysis.

Bill Cutler, Palatine, Illinois

Bill's Baffling Burr (BBB) - the design which appeared in Scientific American (with one piece wrong). It has 24 assemblies, but a unique level-5 solution.

BB43-143M-1 - a level-4, 3-hole design discovered by a computer program which analyzed assemblies made with a fairly limited set of pieces. This is the highest level design I have discovered so far using only the computer. The program only investigated a small fraction of the vast number of designs possible.

BB31-147-1 - a computer discovered level-3 solution with only one hole. A large number of similar designs were found.

BB31-10-40 - another level-3, 1-hole computer discovered design. This one is the `least un-notchable' of the large number of such solutions discovered; it requires only two unit cubes to be glued onto the otherwise notchable pieces.

Bill's Ball Bearing Burr - take the design as shown; add two ball bearings with diameter slightly less than one unit; place one into each of the double cube holes in the solution. The reader can deduce how the puzzle is meant to be taken apart!

Impossible Second Move - this design is only included because it illustrates the computer program's ability to continue disassembling the burr after the first piece or pieces have been removed. The design came up when trying to determine `fitting constraints' for pieces usable in solid solutions. This is as close to a solid solution that the piece numbered `2' can get.

Phillipe DuBois, Israel

Gaby Games 7-move - has two assemblies and one solution. The computer program classifies this as a level-6 solution, although most people would say it has seven moves to take out the first piece.

Victor Goedicke, Athens

Professor Goedicke sent me several very interesting designs, two of which were 6-piece burrs, and the others were more complicated designs with half-notches. The design printed in this booklet has a unique level-3 solution.

Lester Henderson, Danville, California

Lester's design was sent to me by Professor Goedicke. It has more than one solution.

Bruce Love, New Zealand

Bruce sent me no fewer than 15 different holey-6 designs. He also lays claim to a more complicated burr design with a level-13 solution. I include three of his designs in this document:

Love #1 (first design received) - with length six pieces has 14 assemblies with one level-4 solution and five level-5 solutions. With length 8 pieces, there are two level-5 solutions. This design does not have any low-level solutions.

Love Model - The first design I received which the computer classified as level-7. The solution is unique. That the design had this many levels was discovered by Edward Hordern - I had thought this model he had sent me was `just' another one of his level-5 designs!

Love B.4 - I chose this from Bruce's many other designs because it has a unique level-5 solution with length 8 (or longer) pieces. I believe this is the highest level I have received for length-8 piece designs with a unique solution. The solution is also noteworthy because the first move involves a piece which may move more than one unit, but the second move requires the first move be made only one unit in length.

Derwin Brown, Norton, Massachusetts

Derwin sent me two designs, both of which have level-6 solutions. The first has another solution (computer output not included), but for the second the level-6 solution is unique.

William Meek, Hemlock, Michigan

Twist Burr - Bill's design has two pieces with rounded sections. The computer output lists only one assembly, which it cannot take apart. The computer would not be able to take it apart even if the rounded parts were very much smaller, as it cannot rotate pieces.

R. von Randow, West Germany

This design was discovered while trying to make the incorrectly pictured pieces in Scientific American work. The resulting design works essentially the same as does the correct BBB.

Jean Mourik, United Kingdom

Jean's entry has 31 assemblies, only one of which has no solution. The computer output only lists the number of solutions at each level and picture of the highest level solution. The masochistic reader can see if he can duplicate the computer's gyrations (or, worse for me, find that it is in error).

Richard Korsmeyer, Oak Ridge, Tennessee

Dick proposed a slight change to one of the Gaby Games pieces - the resulting design has three level-5 solutions.

Peter Marineau, Troy, New York

Having seen many level-5 designs, a few level-6 designs, and one level-7 design to this point, I was prepared to declare Bruce Love's level-7 design as the best (at least from the program's point of view), when along came two designs from a new source. The first has level-3 and level-4 solutions, but the second has a UNIQUE LEVEL-9 SOLUTION. I am reminded of Bob Beamon's long-jump record in the 1976 Olympics! The complete output from this design is included.

L. Edward Hordern, England

Edward proposed a modification to Peter Marineau's design which increases the level to ten. Unfortunately, 12 new low-level solutions are introduced, so the solution is not unique.

I do not expect the designs to end here. I fully expect that more holey-6 designs will be produced, with many more surprises!

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