Sources page biographical material

6.W.2. SIX PIECE BURR = CHINESE CROSS
The usual form of these has six sticks, 2 x 2 x 6 (or 8), which have various notches in them. In the 1990s, new forms were introduced, using plates or boards. One version makes an open frame shape, something like a 3 x 3 x 3 chessboard. In the other, 1 x 4 x 6 boards are paired side by side and the result looks like a classic six-piece burr with the end rectangle divided lengthwise rather than crosswise. See also 6.W.7.
Jurgis Baltrušaitis. Anamorphoses ou magie artificielle des effets merveilleux. Olivier Perrin Éditeur, Paris, 1969. On pp. 110-116 & 184 is a discussion of a 1698 engraving "L'Académie des Sciences et des Beaux Arts" by Sébastien Leclerc (or Le Clerc). In the right foreground is an object looking like a six piece burr. James Dalgety discusses this in his Latest news on oldest puzzles; Lecture to Second Meeting on the History of Recreational Mathematics, 1 Jun 1996. This image also exists in a large painted version (950 x 480 mm) which is more precise and more legible in many details, so it is supposed that the engraving was done in conjunction with the painting. Though it was normal for a notable painting to be turned into an engraving, the opposite sometimes happened and Leclerc was a famous engraver. The painter is unknown. The divisions between the pairs of pieces of the 'burr' are pretty clear in the engraving, but two of them are not visible in the painting. The 'burr' is also not quite correctly drawn, but all in all, it seems pretty convincing. James Dalgety was the first to discover this picture and he has a copy of the engraving, but has not been able to locate the painting, though it was in the Bernard Monnier Collection exhibited at the Musée des Arts Decoratifs in Paris in 1975/76.

Camille Frémontier. Sébastien Leclerc and the British Encyclopeaedists. Sphæra [Newsletter of the Museum of the History of Science, Oxford] 6 (Aut 1997) 6-7. Discusses the Leclerc engraving which was used as the frontispiece to several encyclopedias, the earliest being Chambers Cyclopaedia of 1728.

Minguet. 1733. Pp. 103-105 (1755: 51-52; 1822: 122-124; 1864: 103-104). Pieces diagrammed. One plain key piece.

Catel. Kunst-Cabinet. 1790. Die kleine Teufelsklaue, p. 10 & fig. 16 on plate I. Figure shows it assembled and fails to draw one of the divisions between pieces. Description says it is 6 pieces, 2 inches long, from plum wood and costs 3 groschen (worth about an English penny of the time). (See also pp. 9-10, fig. 20 on plate I for Die grosse Teufelsklaue -- the 'squirrelcage'.)

Bestelmeier. 1801. Item 147: Die kleine Teufelsklaue. (Note -- there is another item 147 on the next plate.) Only shows it assembled. Brief text may be copying part of Catel. See also the picture for item 1099 which looks like a six piece burr included in a set of puzzles. (See also Item 142: Die grosse Teufelsklaue.)

Edward Hordern's collection has examples, called The Oak of Old England, from c1840.

Crambrook. 1843. P. 5, no. 5: Maltese Cross 6 [pieces], three sorts. Not clear if these might be here or in 6.W.4 or 6.W.5 -- ??

Magician's Own Book. 1857. Prob. 1: The Chinese cross, pp. 266-267 & 291. One plain key piece. Not the same as in Minguét.

Landells. Boy's Own Toy-Maker. 1858. Pp. 137-139. Identical to Magician's Own Book.

Book of 500 Puzzles. 1859. 1: The Chinese cross, pp. 80-81 & 105. Identical to Magician's Own Book.

A. F. Bogesen (1792 1876). In the Danish Technical Museum, Helsingør (= Elsinore) are a number of wooden puzzles made by him, including a 6 piece burr, a 12 piece burr, an Imperial Scale? and a complex (trick??) joint.

Illustrated Boy's Own Treasury. 1860. Practical Puzzles, No. 23: The Chinese Cross, pp. 399 & 439. Identical to Magician's Own Book, except one diagram in the solution omits two labels.

Boy's Own Conjuring Book. 1860. Prob. 1: The Chinese cross, pp. 228 & 254. Identical to Magician's Own Book.

Hoffmann. 1893. Chap. III, no. 36: The nut (or six piece) puzzle, pp. 106 & 139 140 = Hoffmann-Hordern, pp. 104-106. Different pieces than in Minguét and Magician's Own Book.

Dudeney. Prob. 473 -- Chinese cross. Weekly Dispatch (23 Nov & 7 Dec 1902), both p. 13. "There is considerable variety in the manner of cutting out the pieces, and though the puzzle has been given in some of the old books, I have purposely presented it in a form that has not, I believe, been published."

Dudeney. Great puzzle crazes. Op. cit. in 2. 1904. "... the "Chinese Cross," a puzzle of undoubted Oriental origin that was formerly brought from China by travellers as a curiosity, but for a long time has had a steady sale in this country."

Wehman. New Book of 200 Puzzles. 1908. The Chinese cross, pp. 40-41. = Magician's Own Book.

Dudeney. The world's best puzzles. 1908. Op. cit. in 2. P. 779 shows a '"Chinese Cross" which ... is of great antiquity.'

Oscar W. Brown. US Patent 1,225,760 -- Puzzle. Applied: 27 Jun 1916; patented: 15 May 1917. 3pp + 1p diagrams. Coffin says this is the earliest US patent, with several others following soon after.

Anon. Woodwork Joints, 1918, op. cit. in 6.W.1. Eastern joint puzzle, pp. 196 197: Two versions using different pieces. Six piece joint puzzle, pp. 199 200. Another version.

Western Puzzle Works, 1926 Catalogue. No. 86: 6 piece Wood Block. Several other possible versions -- see 6.W.7.

E. M. Wyatt. Six piece burr. Puzzles in Wood, 1928, op. cit. in 5.H.1, pp. 27 28. Describes 17 versions from 13 types of piece.

A. S. Filipiak. Mathematical Puzzles, 1942, op. cit. in 5.H.1, pp. 79 87. 73 versions from 38 types of piece.

William H. [Bill] Cutler. The six piece burr. JRM 10 (1977 78) 241 250. Complete, computer assisted, analysis, with help from T. H. O'Beirne and A. C. Cross. Pieces are considered as 'notchable' if they can be made by a sequence of notches, which are produced by two saw cuts and then chiselling out the space between them. Otherwise viewed, notches are what could be produced by a wide cutter or router. There are 25 of these which can occur in solutions. (In 1994, he states that there are a total of 59 notchable pieces and diagrams all of them.) One can also have more general pieces with 'right-angle notches' which would require four chisel cuts -- e.g. to cut a single 1 x 1 x 1 piece out of a 2 x 2 x 8 rod. Alternatively, one can glue cubes into notches. There are 369 which can occur in solutions. (In 1994, he states that there are 837 pieces which produce 2225 different oriented pieces, and he lists them all.) He only considers solid solutions -- i.e. ones where there are no internal holes. He finds and lists the 314 'notchable' solutions. There are 119,979 general solutions.

C. Arthur Cross. The Chinese Cross. Pentangle, Over Wallop, Hants., UK, 1979. Brief description of the solutions in the general case, as found by Cutler and Cross.

S&B, p. 83, describes holey burrs.

W. H. [Bill] Cutler. Christmas letter, 1987. Sketches results of his (and other's) search for holey burrs with notchable pieces.

Bill Cutler. Holey 6 Piece Burr! Published by the author, Palatine, Illinois. (1986); with addendum, 1988, 48pp. He is now permitting internal holes. Describes holey burrs with notchable pieces, particularly those with multiple moves to release the first piece.

Bill Cutler. A Computer Analysis of All 6-Piece Burrs. Published by the author, ibid., 1994. 86pp. Sketches complete history of the project. (I have included a few details in the description of his 1977/78 article, above.) In 1987, he computed all the notchable holey solutions, using about 2 months of PC AT time, finding 13,354,991 assemblies giving 7.4 million solutions. Two of these were level 10 -- i.e. they require 10 moves to remove the first piece (or pieces), but the highest level occurring for a unique solution was 5. After that he started on the general holey burrs and estimated it would take 400 years of PC AT time -- running at 8 MHz. After some development, the actual time used was about 62.5 PC AT years, but a lot of this was done on by Harry L. Nelson during idle time on the Crays at Lawrence Livermore Laboratories, and faster PCs became available, so the whole project only took about 2½ years, being completed in Aug 1990 and finding 35,657,131,235 assemblies. He hasn't checked if all assemblies come apart fully, but he estimates there are 5.75 billion solutions. He estimates the project used 45 times the computing power used in the proof of the Four Color Theorem and that the project would only take two weeks on the eight RS6000 workstations he now supervises. Some 70,000 high-level solutions were specifically saved and can be obtained on disc from him. The highest level found was 12 and the highest level for a unique solution was 10. See 6.W.1 for a continuation of this work. He has a website with many of his results on burrs, etc.: www.billcutlerpuzzles.com .

Bill Cutler & Frans de Vreugd. Information leaflet accompanying their separate IPP22 puzzles, 2002. In 2001, they did an analysis of six-board burrs, of the type where the boards are paired side by side. There are 4096 possible such boards, but only 219 usable boards occur. They looked at all combinations of six of these and found 14,563,061,989 assemblies. Of these, the highest level found was 13.