SOLID and HOLEY SIX-PIECE BURR PUZZLES

The BURR puzzle has also been known as
THE CHINESE CROSS, THE MALTESE CROSS and THE JACK PUZZLE.

Early examples are known from the late 18th century. Versions in ivory have been imported to Europe from China since the early 1800s. Most of the early versions were based on the same design.

The standard rule is that there are only 6 pieces and that grooves in the pieces are always cut half way into the piece.

Many people have done work on the puzzle but Bill Cutler and Arthur Cross completed a comprehensive analysis of the solid puzzle in 1975.

 


Limiting pieces to those which can be cut out with a saw and therefore contain no "blind corners", there are 26 useable pieces which can be built into the puzzle in 314 different ways without internal spaces.*

Allowing pieces with "blind corners" (either a chisel must be used, or a unit cube glued into a groove during manufacture), there are 369 different usable pieces that can be made into 119,979 different 6 piece puzzles without internal spaces.

Some puzzles have a key piece, some separate into groups of 2 & 4 pieces, and some come apart as two groups of 3 pieces. Some have several solutions and some only one. One puzzle has 6 solutions.

 

If internal spaces are permitted, a more interesting puzzle can be constructed, in which it is necessary to make several moves before the first piece can be removed. These are known as "Holey 6 Piece Burrs".

On August the 4th 1990 the last Holey 6 Piece Burr was analyzed by Bill Cutler. Over a two year period various people gave computer time to the project and at one stage a Cray computer was used. It took 62.5 years of computing time running at 8 MHz., which was then the standard speed of a PC, to analyze all 35,657,131,235 puzzles.

Solutions were given a "Level" number corresponding to the number of moves required before the first piece can be removed. Of particular interest is the fact that the only Level 12 puzzle was discovered by Bruce Love using his own human brain several years earlier.

The results of the more complex puzzles were: -

 

Level
Total Puzzles
Puzzles with unique solutions
12
10
9
8
1
373
6792
60784

0
18
355
5254

18 September 1990 J.Dalgety

This Compendium of 42 pieces was made by Pentangle from 1979 and included the duplicate and triplicate pieces required to assemble any of the 314 puzzles. This raised the question of what is the largest number of puzzles that can be assembled at one time from the compendium. It turns out that there are 2075 ways to assemble 5 puzzles at one time from the set of 42 pieces. An example of 5 simultaneous assemblies, using Arthur Cross's notation) is AMUUWX-BEMWXY-BOQRTY-DGIIVY-DJORTV. JCD 4/94)


Akio Kamei made a set in 1987 which looked as if it contained 45 pieces. Actually it was a set of 52 pieces with 7 extra pieces hidden inside. This made it a packing puzzle.

Here are some examples of how to change the appearance of a Six Piece Burr Puzzle

July 2012

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