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This section contains many examples of 6-piece burrs. A brief description is given below, including date of design, designer, and method of design. Love's Dozen, Computer's Choice Unique-10, and Programmer's Nightmare are described in detail. For other standard 6-piece burr designs, consult Table 12 and the LL Format description to see how the pieces fit together.

Bill's Baffling Burr - March 3, 1984 - unique level-5 - Bill Cutler - probably the first "computer-assisted" burr design, this was described in the Computer Recreations column of Scientific American [6]. Unfortunately, the picture of one of the pieces was incorrect (corrected in some foreign language editions).

The Piston Puzzle - 1986 - unique level-9 - Peter Marineau came up with this design by hand. Before this design, the highest unique solution known was level-7.

L5 Notchable - 1987 - unique level-5 - exhaustive computer search by Bill Cutler - the highest level for unique solutions in notchable 6-piece burrs is 5. This is one of 139 such designs.

Love's Dozen - 1987 - non-unique level-12 - Bruce Love - Using the definition of level in this booklet, this is the highest level possible to remove the first piece in a 6-piece burr, and there are no other level-12's and no level-11's at all.
Love's Dozen LL Format to Assembly
Love's Dozen Computer Output

Computer's Choice 3-Hole - 1988 - unique level-7 - exhaustive computer search by Bill Cutler & others - after the completion of the analysis of all 2.5 billion 3-hole assemblies, one was chosen as the best. The major requirements were highest level and unique. 198 level-7 3-hole solutions were found, of which 157 are unique.

Computer's Choice 4-Hole - 1988 - unique level-8 - exhaustive computer search by Bill Cutler & others - of the 4.7 billion 4-hole assemblies, 15 are level-8, with 13 of these being unique.

Diagram of the previous 6 puzzles

Programmer's Nightmare - 1989 - Bill Cutler computer-assisted design -
Programmer's Nightmare Solution
Programmer's Nightmare Three Close Solutions
Programmer's Nightmare Rotation in Legal Solution

Bill's Ball-Bearing Burr - 1986 - level-3 + 'trick' move - computer-assisted design by Bill Cutler - The idea of inserting ball bearings into the interior of a 6-piece burr gave rise to this puzzle. There are 4 internal cubic-holes on the inside in two pairs of 2 adjacent cubes. The design is such that the balls must be rolled to the outside cubes in each of the holes. This is accomplished by spinning the burr so that centrifugal force is used.

Notchable 1-Hole Level-2 - 1987 - computer search by Bill Cutler - there are only 4 notchable assemblies with one hole which have a level-2 (or higher) solution. One of them was chosen at random.

Computer's Choice 5-Hole - 1988 - unique level-9 - exhaustive computer search by Bill Cutler & others - of the 6.5 billion 5-hole assemblies, 23 are level-9, with 21 of these being unique.

Computer's Choice Unique 10 - 1990 - unique level-10 - exhaustive computer search by Bill Cutler & others - the highest unique level for a 6-piece burr is 10. There are only 18 such assemblies, all of which disassemble in similar fashions.
Computer's Choice Unique 10 LL Format to Assembly
Computer's Choice Unique 10 Computer Output

Partial Level-6 Solution - 1987 - notchable partial solution only - computer search by Bill Cutler - this is the highest known level for the first disassembly in a partial solution. There are no level-8 partial solutions, and the 692,888 level-7 assemblies were not saved for running this analysis, so it is unknown if there is a partial level-7 solution.

Diagram of the previous 6 puzzles

L46AA Notchable - 1987 - non-unique level-10 - exhaustive computer search by Bill Cutler - the highest level solution for notchable 6-piece burrs is 10. There are two of these, and this is the one with fewer holes.

Most ASM - Unique Level-8 - 1990 - computer search - largest number of assemblies (111) for a unique solution, level-8 or higher.

Most ASM - Notchable Unique Level-5 - 1987 - computer search - largest number of assemblies (480) for a notchable, unique solution, level-5 or higher.

Different at Lengths 10 & 12 - 1987 - Bruce Love - Many 6-piece burr assemblies have different solutions at lengths of pieces 6, 8 and 10, but few have any difference beyond length 10. What is the longest length for which this difference can exist? I asked this question in [5]. Both Bruce Love and Peter Marineau gave examples of assemblies where there is a difference between length 10 and length 12 pieces. There are no differences past length 12.

The 139 Burr - 1989 - impossible object - Bill Cutler & Jerry McFarland - during the course of the 6-piece burr analysis, I kept track of the number of states that were found in analyzing an assembly. There were only a few which passed the 100 mark, and some of these would not disassemble at all. The largest number of states that can be achieved without coming apart is 139. Several notchable 6-piece burrs with length10 pieces have this property. I chose one of these and challenged Jerry to manufacture them in some way. They were given out as my souvenir for the 10th International Puzzle Party held in London on August 27, 1989.

Diagram of the previous 5 puzzles

U-Nam-It Burr - 1989 - Bill Cutler - Diagram of U-Nam-It

Explode-A-Burr - 1965 - Bill Cutler - souvenir of the 13th International Puzzle Party in the Netherlands, 1993 - Diagram of Explode-A-Burr

The Weave - ???????????? Diagram of The Weave

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