11

11. TOPOLOGICAL RECREATIONS

Many of the puzzles described here have the common characteristic that a loop of string is entangled in some object and the entangled string has to be worked through a number of holes in order to remove the string or to release a ring, etc.

In 11.I, the end of the loop is worked through holes until it can be looped around the other end of the string which has an obstructive object on it. Alternatively, the loop can be passed round the object containing the holes. Which is easier depends on the relative sizes of the two objects involved.

In 11.A, the other end of the loop is inaccessible and the end of the loop is then passed around the object, which is equivalent to passing it over the other end of the loop.

In 11.E, the other end of the loop is inaccessible and the end of the loop must be partly passed over the deformable object to allow the obstruction to pass through the deformed object. 11.I, 11.A and 11.E are thus all based on the reef or square knot and topologically equivalent. Some of the trick purses in 11.F use this idea.

In 11.B, the basic process is obscured by using people so that one does not readily see the necessary path. 11.H are 11.H.1 are essentially the same as this, both in their topology and their obscuring process. The wire puzzle called The United Hearts, Cupid's Bow, etc. is isomorphic to this.

In 11.C, the basic process is obscured by using a flexible object which is deformed to act as the loop.

In 11.F, the basic process is again obscured, this time by the fact that the holes do not appear to be part of the puzzle and by the fact that one does not remove the loop, but instead a ring is released.

11.D is somewhat similar, but the process of moving the end of the loop is quite different and the object is to move objects along the string, so this is basically a different type of puzzle.

7.M.5 is in this general category, but the systematic binary pattern of disentanglement makes it quite different from the items below.

11.A. SCISSORS ON STRING

Ozanam. 1725. Vol. IV, prob. 35, p. 437 & fig. 42, plate 18 (error for 13) (15).

Minguét. Engaños. 1733. Pp. 108-109 (1755: 76-77; 1822: 83-84 & 127-128). Somewhat similar to Ozanam.

Alberti. 1747. Art. 35, p. 209 (110) and fig. 43, plate XII, opposite p. 212 (110). Taken from Ozanam.

Manuel des Sorciers. 1825. Pp. 210-211, art. 25.

The Sociable. 1858. Prob. 40: The scissors entangled, pp. 298 & 316. "This is an old but a capital puzzle." Says the ends are held in the hand, but figure shows them tied to a post. = Book of 500 Puzzles, 1859, prob. 40, pp. 16 & 34. See Magician's Own Book (UK version) for a clearer version. = Wehman, New Book of 200 Puzzles, 1908, p. 44.

Indoor & Outdoor. c1859. Part II, p. 129, prob. 9: The scissors entangled. Almost identical to The Sociable, but the figure omits the post and the problem statement starts with 56. _ apparently the problem number in the source from which this was taken.

Magician's Own Book (UK version). 1871. The liberated prisoner, pp. 211-212. Shows a prisoner chained in this manner, but the diagram is too small to really see what is going on. Then says it is equivalent to the scissors problem, which is clearly drawn and much bigger than in The Sociable. The explanation is clearer than in The Sociable.

Tissandier. Récréations Scientifiques. 1880? 2nd ed., 1881, gives a brief unlabelled description on pp. 330-331, with figure copied from Ozanam on p. 328.

5th ed., 1888, La cordelette et les ciseaux, p. 259. Based on Ozanam, copying the diagram.

The index of the English ed. has a reference which is probably to this, but the relevant page 775 has become the title for the Supplement!

Anonymous. Social Entertainer and Tricks (thus on spine, but running title inside is New Book of Tricks). Apparently a compilation with advertisements for Johnson Smith (Detroit, Michigan) products, c1890?. P. 38b: The scissors trick.

Hoffmann. 1893. Chap. X, no. 46: The entangled scissors, pp. 355 & 393.

A. Murray. Tricks with string. The Boy's Own Paper 17 or 18?? (1894??) 526-527. Well drawn.

Devant. Tricks for Everyone. Op. cit. in 4.A.1. 1910. The scissors trick, pp. 35-36. Simple version.

Adams. Indoor Games. 1912. The tailor's scissors, pp. 28‑30.

Williams. Home Entertainments. 1914. The entangled scissors, pp. 111-112.

Collins. Book of Puzzles. 1927. The dressmaker's puzzle, pp. 21-22.

J. F. Orrin. Easy Magic for Evening Parties. Op. cit. in 7.Q.2. 1930s?? The scissors puzzle, pp. 36-37.

11.B. TWO PEOPLE JOINED BY ROPES AT WRISTS

This is isomorphic to 11.K.8. See von Hartwig, Goldston and Svengarro for one person versions.

Ozanam. 1725. Vol. IV, prob. 38, p. 438 & fig. 45, plate 18 (error for 13) (15).

Minguét. Engaños. 1733. Pp. 110-111 (1755: 77-78; 1822: 129-130). Similar to Ozanam.

Alberti. 1747. Art. 38, p. 212 (111) and fig. 46, plate XII, opposite p. 212 (110). Taken from Ozanam.

Family Friend 2 (1850) 267 & 353. Practical Puzzle _ No. IX. = Illustrated Boy's Own Treasury, 1860, Practical Puzzles, No. 37, pp. 402 & 442.

Parlour Pastime, 1857. = Indoor & Outdoor, c1859, Part 1. = Parlour Pastimes, 1868. Mechanical puzzles, no. 10, pp. 180-181 (1868: 191-192).

Magician's Own Book. 1857. No. 11: The handcuffs, p. 11. = Boy's Own Conjuring Book, 1860, p. 23.

Leske. Illustriertes Spielbuch für Mädchen. 1864? Prob. 177, p. 96: Die verschlungenen Schnüre.

Anonymous. Every Little Boy's Book A Complete Cyclopædia of in and outdoor games with and without toys, domestic pets, conjuring, shows, riddles, etc. With two hundred and fifty illustrations. Routledge, London, nd. HPL gives c1850, but the text is identical to Every Boy's Book, whose first edition was 1856, and which has not yet been entered. In 4.A.1, I've guessed this book may be c1868. Pp. 360-361: The handcuffs.

Magician's Own Book (UK version). 1871. The prisoner's release, pp. 209-211. Adds that one can also intertwine the two cords in the form of a square or reef knot which allows a simpler disentanglement.

Elliott. Within‑Doors. Op. cit. in 6.V. 1872. Chap. 4, no. 13: The handcuffs, p. 97.

Cassell's. 1881. P. 94: The prisoners' release puzzle. = Manson, 1911, 143-144

Tissandier. Récréations Scientifiques. 1880? 2nd ed., 1881, brief unlabelled description on p. 330 with figure copied from Ozanam on p. 328.

5th ed., 1888, Les deux prisonniers, pp. 257-258. Based on Ozanam, copying the diagram.

The index of the English ed. has a reference which is probably to this, but the relevant page 775 has become the title for the Supplement!

Richard von Hartwig. UK Patent 3859 _ A New Game or Puzzle. Applied 27 Feb 1892; accepted 2 Apr 1892. 1p + 1p diagrams. One man, the other loop being tied to a tree.

Hoffmann. 1893. Chap. X, no. 36: Silken fetters, pp. 349‑350 & 390.

A. Murray. Tricks with string. The Boy's Own Paper 17 or 18?? (1894??) 526-527.

Adams. Indoor Games. 1912. Release the prisoners, pp. 28‑29.

Will Goldston. The Young Conjuror. [1912 _ BMC]; 2nd ed., Will Goldston Ltd, London, nd [1919 _ NUC], Vol. 1, pp. 34-39: Three Malay rope tricks. No. two is the present section, with one person having his wrists tied and a string looped around and held by another person. Golston thanks E. R. Bartrum for the text and illustrations.

Prof. Svengarro. Book of Tricks and Magic. I. & M. Ottenheimer, Baltimore, 1913. Rope trick, p. 15. As in Goldston, with wrists tied by a handkerchief and then a rope looped around it.

Williams. Home Entertainments. 1914. The looped chains, pp. 109-110. Jailer tries to secure prisoner by this method.

J. F. Orrin. Easy Magic for Evening Parties. Op. cit. in 7.Q.2. 1930s?? The magic release (no. 1), pp. 26-27.

McKay. Party Night. 1940. How did it get there?, p. 150. This is an alternate method which gives a 'knot' between the two strings. It is most easily described from the undone state and the second loop is most easily visualised as a ring. Form a bight in the string and pass it through the ring, then pass it under the loop around one wrist, over the hand and back under the loop. This leaves the bight around the wrist below the loop. Now just lift it off the hand and the string will be knotted to the ring.

11.C. TWO BALLS ON STRING THROUGH LEATHER HOLE AND

STRAP = CHERRIES PUZZLE

The basic version has a leather strap with two longish cuts allowing the central part to flex away from the rest of the strap. There is a hole at the bottom of the strap. A string with balls at each end comes through the hole and around the central part. The balls are larger than the hole, but the central part can be brought through the hole to form a loop big enough to pass a ball through.

The balls were often called cherries and even drawn as such. I wonder if the puzzle originally used a pair of joined-together cherries??

An equivalent version has a slit in a card (sometimes tubular), producing a thin part on which hangs the string with two balls with a ring or cylinder about the double string. A variation of this has a doubled paper or leather object such as a pair of boots attached at the tops, with just a paper loop or annulus around it. The key to these versions is folding the card so the thin bit can be brought through the ring, cylinder or loop.

Schwenter. 1636. Part 10, exercise 30, p. 411. Version using a card.

Witgeest. Het Natuurlyk Tover-Boek. 1686.

Prob. 18, pp. 160-161. Elaborate card version.

Prob. 19, pp. 162-163. Cherries.

Ozanam. 1725.

Vol. IV, prob. 30, p. 434 & fig. 36, plate 11 (13). Version using a tube.

Vol. IV, prob. 33, p. 436 & fig. 39, plate 12 (14). "On peut passer des queues de Cerises dans un papier, ...."

Minguét. Engaños. 1733. Pp. 112-113 (1755: 79; 1822: 131-132). Cherries version. Similar to Ozanam, prob. 33.

Alberti. 1747. Loc. cit. in 11.A.

Art. 30, pp. 204‑205 (108) and fig. 37, plate X, opp. p. 206 (between pp. 108 & 109) Version using a tube. Taken from Ozanam.

Art. 33, pp. 207-208 (109‑110) and fig. 40, plate XI, opp. p. 210 (109). "Si possono passare dai gambi di cerase in una carta....". Taken from Ozanam.

Catel. Kunst-Cabinet. 1790. Die verbundenen Kirschen, pp. 13-14 & fig. 18 on plate I.

Bestelmeier. 1801. Item 273: Der verschlungenen Kirschen. Copies part of Catel's text.

Manuel des Sorciers. 1825. Pp. 182-183: Le jeu des cerises.

The Boy's Own Book.

The cherry cheat. 1828: 418; 1828-2: 423; 1829 (US): 215; 1855: 570; 1868: 672.

The card puzzle. 1828: 422‑423; 1828-2: 427-428; 1829 (US): 219; 1855: 574; 1868: 676. Version with a tube. c= Magician's Own Book, 1857. = Wehman, New Book of 200 Puzzles, 1908, pp. 38-39.

Child. Girl's Own Book. Heart, dart, and key. 1833: 138-139; 1839: 122-123; 1842: 203‑204. A variation of the card version with the key as the ring. Cf Magician's Own Book (UK version).

Nuts to Crack II (1833), no. 92. The card puzzle. Almost identical to Boy's Own Book.

Crambrook. 1843. P. 4, no. 16: Cherry Cheat Puzzle. Check??

Family Friend 2 (1850) 208 & 239. Practical Puzzle, No. VII. Repeated as Puzzle 10 _ The button puzzle in (1855) 339 with solution in (1856) 28 . = The Illustrated Boy's Own Treasury, 1860, Practical Puzzles, No. 43, pp. 403 & 442. Identical to Magician's Own Book, prob. 11. Cherries puzzle using buttons.

Magician's Own Book. 1857.

Prob. 11: The button puzzle, pp. 269 & 294. Identical to Family Friend with slight changes of wording. = Wehman, New Book of 200 Puzzles, 1908, p. 15.

Prob. 19: The card puzzle, pp. 272-273 & 296. Identical to Boy's Own Book card puzzle, except the answer is split from the problem, but the problem refers to the figures which are now in the answer!

Book of 500 Puzzles. 1859.

Prob. 11: The button puzzle, pp. 83 & 108. Identical to Magician's Own Book.

Prob. 19: The card puzzle, pp. 86-87 & 110. Identical to Magician's Own Book.

Boy's Own Conjuring Book. 1860.

Prob. 10: The button puzzle, pp. 230 & 257. Identical to Magician's Own Book.

Prob. 18: The card puzzle, 234 & 259. Identical to Magician's Own Book.

Magician's Own Book (UK version). 1871.

The string and button puzzle, p. 326.

Key, heart, and dart, pp. 232-233. A variation of the card version with the key as the ring. Cf Girl's Own Book, but this has much better pictures and different text. Card version with key as the ring.

Elliott. Within‑Doors. Op. cit. in 6.V. 1872. Chap. 1, no. 10: The button puzzle, pp. 29 & 31.

Hanky Panky. 1872. The undetachable cylinder, pp. 125‑126. Card version.

Martin Appleton Wright. UK Patent 7002 _ Improved Advertisement Cards. Dated 28 Apr 1884 and 30 Apr 1884. 1p + 2pp diagrams. Card versions.

William Crompton. The odd half-hour. The Boy's Own Paper 13 (No. 657) (15 Aug 1891) 731-732. The slippery buttons.

Handy Book for Boys and Girls. Op. cit. in 6.F.3. 1892. Pp. 57-59: The boot puzzle. Card version with a pair of boots.

Tom Tit, vol. 3. 1893. Le jeu de la fève, pp. 225-226. = K, no. 171: The bean trick, pp. 394‑395. Card version, using a bean pod to make all the parts.

Hoffmann. 1893. Chap. II, no. 24: The ball and three strings, pp. 34‑35 & 59‑60. This is a more complex puzzle, but based on the same principle. A string goes around other strings, through a ball and then has ends separately knotted, so you have to bring the other strings through the ball in order to release the string.

Benson. 1904. The ball and strings puzzle, p. 217. As in Hoffmann.

Williams. Home Entertainments. 1914. String and button puzzle, p. 112. Cherries puzzle using buttons.

Collins. Book of Puzzles. 1927. The bachelor's button puzzle, pp. 22-23.

A. B. Nordmann. One Hundred More Parlour Tricks and Problems. Wells, Gardner, Darton & Co., London, nd [1927 _ BMC]. No. 88: The button trick, pp. 80-82. This is a card version, but with a string and buttons. The card has two long parallel cuts, as in the leather version, but it then has two slots off to the side that the string goes through. One has to fold the card to superimpose these two slots, then fold it again to bring the thin strip to these slots.

11.D. SOLOMON'S SEAL

See S&B, p. 114. Slocum and Gebhardt have pointed out that there are two approaches to this problem, particularly in the two ball case, depending on how the ends of the string are attached to the board. If the string is passed through a hole and a knot is tied in the string, rather than tying the string to the board, then one can partially undo the central loop by passing it through the end hole and around the end of the string _ repeating with a slight change completely undoes the central loop. This approach makes the problem really a form of 11.I. However, I think that in most cases with a knot in the string, the indicated size of the hole in the board is too small to permit a loop to pass through and this method is not possible.

Pacioli. De Viribus. c1500. Ff. 206v-207r, Part 2, Capitolo CI: De un altro filo pur in 3 fori in la stecca con unambra per sacca far le andare' tutte in una. The chapter titles vary between the actual problem and the Table of Contents and the latter shows that 'unambra' should be 'una ambra'. Sacca means pocket or bay or inlet and it seems clear he means a loop which has that sort of shape. Ambra is amber, but seems to mean an amber bead here. So the chapter title can be translated as: On another string also in three holes in the stick with one bead per loop, make all of them go onto one. Sadly there is no picture.

Schwenter. 1636. Part 10, exercise 27, pp. 408-410. With two rings.

Witgeest. Het Natuurlyk Tover-Boek. 1686. Prob. 43, pp. 33-34. Clearly taken from Schwenter.

Ozanam. 1725. Vol. IV, prob. 40, pp. 439‑440 & fig. 47, plate 14 (16). Le Sigillum Salomonis, ou Sceau de Salomon _ version with four rings.

Alberti. 1747. Art. 40, pp. 214 (112) and fig. 48, plate XIII, opposite p. 214 (111). Il Sigillum Salomonis, o Sigillo Salomone _ version with 4 rings. Taken from Ozanam.

Catel. Kunst-Cabinet. 1790. Die Salomonsringe, pp. 14-15 & fig. 24 on plate I. Version with 4 rings. Describes how to solve it.

Bestelmeier. 1801. Item 214: Die Salomons‑Ringe. Version with 3 rings. Brief text.

Boy's Treasury. 1844. Puzzles and paradoxes, no. 14: The bead puzzle, pp. 426 & 430. "This puzzle may be procured at many toy-shops."

Family Friend 3 (1850) 30 & 61. Practical puzzle _ No. XI. Love's Puzzle with two hearts. = The Sociable, 1858, Prob. 24: Love's Puzzle, pp. 294 & 310. = Book of 500 Puzzles, 1859, prob. 24, pp. 12 & 28.

Magician's Own Book. 1857. Prob. 37: The string and balls puzzle, pp. 277-278 & 301. Two balls. = Boy's Own Conjuring Book, 1860, prob. 36, pp. 240-241 & 265. = Wehman, New Book of 200 Puzzles, 1908, p. 9.

Book of 500 Puzzles. 1859.

Prob. 24: Love's Puzzle, pp. 12 & 28. As in Family Friend.

Prob. 37: The string and balls puzzle, pp. 91-92 & 115. Identical to Magician's Own Book.

The Illustrated Boy's Own Treasury. 1860. Practical Puzzles, No. 5: Love's puzzle, pp. 396 & 436. Identical with Family Friend.

Magician's Own Book (UK version). 1871. The puzzle of Cupid, p. 227. Two hearts. Diagram is hard to make out.

Elliott. Within‑Doors. Op. cit. in 6.V. 1872. Chap. 1, no. 11: The string and balls, pp. 29 & 31.

Cassell's. 1881. P. 90: The string and balls puzzle. = Manson, 1911, p. 147. Version with 2 balls.

Hoffmann. 1893. Chap. II, no. 13: The two balls, pp. 27‑28 & 53‑54. Photo in Hordern, p. 22.

Burnett Fallow. An ingenious bead puzzle. The Boy's Own Paper 15 (No. 755) (1 Jul 1893) 638. Shows two loop version but notes it can be extended.

Collins. Book of Puzzles. 1927. The string and ball puzzle, pp. 23-24.

James Dalgety. Email of 3 Sep 1999. Reports that his father saw the puzzle in use by Inuits in the Canadian Arctic or Greenland in c1930, but his family lost the walrus ivory (or bone) and leather examples that his father brought back. Also that a collection of topological puzzles from near Lake Tanganyika, gathered in the 1920s and now in the Horniman Museum, London, does not contain an example of Solomon's Seal.

Ch'ung‑En Yü. Ingenious Ring Puzzle Book. 1958. Op. cit. in 7.M.1. P. 28 shows a version, called Double Coin Ring Puzzle.

Fred Grunfield. Games of the World. Ballantine, NY, 1975. On p. 267, he calls this "African String Game", but gives no reference.

Pieter van Delft & Jack Botermans. Creative Puzzles of the World. Abrams, New York, 1978. African ball puzzles. "It was once used in magic rites by tribes living in the jungles of the Ivory Coast. The puzzle is still used for amusement in this part of Africa, not only by the people who inhabit the remote outlying areas but also by city dwellers. ... The puzzles were not restricted to this part of Africa. Variations may be found in Guinea, and some ... were made in China." No reference given, but I suspect it must come from: Charles Beart; Jeux et Jouets de L'Ouest Africain; 2 vols., IFAN, Dakar, 1955, although this is not listed in their bibliography. My thanks to Mark Peters for the reference to van Delft and Botermans.

11.E. LOYD'S PENCIL PUZZLE

See S&B, p. 114. I have seen it claimed that the phrase 'to buttonhole someone' derives from the use of this.

Devant. Tricks for Everyone. Op. cit. in 4.A.1. 1910. The flexible pencil, pp. 13-15. No history.

Will Goldston. More Tricks and Puzzles without Mechanical Apparatus. Op. cit. in 6.AK. 1910?. The pencil, loop and buttonhole, pp. 69‑71.

W. P. Eaton. Loc. cit. in 1. 1911. Gives Loyd's narration of the invention of this for John A. McCall, President of the New York Life Insurance Co.

A. C. White. Sam Loyd and His Chess Problems. 1913. Op. cit. in 1. P. 103. Quotes from Eaton.

A. B. Nordmann. One Hundred More Parlour Tricks and Problems. Wells, Gardner, Darton & Co., London, nd [1927 _ BMC]. No. 87: Latch key trick, pp. 79-80 & 111. This is the only version I have seen using something other than a pencil. It has the advantage that a key has a loop at the end to tie the loop of string to, but the buttonhole will have to be large!

Rohrbough. Puzzle Craft. 1932. The Buttonholer, p. 4 (= p. 4 of 1940s?).

Abraham. 1933. Prob. 165 _ Pencil and buttonhole, pp. 77 (49).

J. F. Orrin. Easy Magic for Evening Parties. Op. cit. in 7.Q.2. 1930s?? Looping the loop, pp. 34-36. No mention of Loyd.

Slocum. Compendium. Shows Magic Coat Pencil from Johnson Smith 1937 catalogue.

Depew. Cokesbury Game Book. 1939. Lapel needle, p. 167. No mention of Loyd.

"Willane". Willane's Wizardry. Academy of Recorded Crafts, Arts and Sciences, Croydon, 1947. The looped pencil, pp. 10-11.

Gardner. SA (Nov 1971) = Wheels, Chap. 12.

11.F. THE IMPERIAL SCALE

This could be combined into 11.I.

Catel. Kunst-Cabinet. 1790. Das einfache Ringspiel, p. 13 & fig. 39 on plate II.

Bestelmeier. 1801. Item 199: Das einfache Ringspiel. Copies part of Catel's text.

The Boy's Own Book. The scale and ring puzzle. 1828: 424‑425; 1828‑2: 429; 1829 (US): 220-221; 1855: 575; 1868: 677-678.

Nuts to Crack III (1834), no. 82. The scale and ring puzzle. Almost identical to Boy's Own Book.

Crambrook. 1843. P. 4, no. 8: Imperial Scale. Check??

Boy's Treasury. 1844. Puzzles and paradoxes, engraved heading of the section, p. 424, shows the puzzle.

See Bogesen, 6.W.2, for an actual example, mid 19C.

Magician's Own Book. 1857. Prob. 15: The scale and ring puzzle, pp. 270-271 & 295. Identical to Boy's Own Book, but with an illogical break between puzzle and solution. = Book of 500 Puzzles, 1859, pp. 84-85 & 109. = Boy's Own Conjuring Book, 1860, prob. 14, pp. 232‑233 & 258. = Magician's Own Book (UK version), 1871, pp. 229‑230. c= Wehman, New Book of 200 Puzzles, 1908, p. 23, which omits the solution, which is not really needed.

F. Chasemore. Loc. cit. in 6.W.5. 1891. Item 1: The balance puzzle, p. 571.

Hoffmann. 1893. Chap. II, no. 19: The imperial scale, pp. 31‑32 & 56‑57. Photo in Hordern, p. 27.

William Hollins. UK Patent 21,097 _ An Improved Puzzle. Applied 23 Sep 1896; accepted 5 Dec 1896. 1p + 1p diagrams. Identical to all the above!!

11.G. TRICK PURSES

van Etten. 1624. Prob. 60 (55), p. 55 & fig. opp. p. 33 (p. 80).

Schwenter. 1636. Part 15, exercise 18, p, 545. Almost identical to van Etten.

Witgeest. Het Natuurlyk Tover-Boek. 1686. Prob. 33, pp. 25-26. Simlar to van Etten, but with a more decorative purse.

Ozanam. 1725. Vol. IV.

Prob. 32, pp. 435‑436 & fig. 38, plate 12 (14). This has a sliding slit leather tab.

Prob. 39, p. 439 & fig. 46, plate 14 (16). This is based on trick stitching.

Prob. 42, pp. 440‑441 & fig. 49, plate 15 (17). This is like the van Etten example.

Alberti. 1747.

Art 32, pp. 206-207 (109) & fig. 39, plate XI, opp. p. 211 (109). Taken from Ozanam, prob. 32.

Art. 39, pp. 212-213 (111‑112) & fig. 47, plate XIII, opp. p. 214 (111). Based on trick stitching, taken from Ozanam, prob. 39.

Art. 42, pp. 215‑217 (112‑113) and fig. 50, plate XIIII, opp. p. 218 (112). Taken from Ozanam, prob. 52.

Catel. Kunst-Cabinet. 1790.

Die Jägertasche, p. 21 & fig. 35 on plate II. Like Ozanam, prob. 42.

Die Vexierbörse, p. 21 & fig. 22 on plate I. Apparently a trick stitch as in Ozanam, prob. 39.

Bestelmeier. 1801. Item 387: Ein Zauberbeutel. Copies Catel's Jägertasche. Like Ozanam, prob. 42.

Child. Girl's Own Book. 1833: 219-220; 1839: 198-199; 1842: 316. The miser's purse, apparently a trick stitch as in Ozanam, prob. 42, ??

Crambrook. 1843. P. 3. The Miser's Purse; The Ring Purse. These might be trick items??

The Sociable. 1858. Prob. 15: Puzzle purse, pp. 291 & 307. Like Ozanam, 1725, prob. 52 but with a second similar locking mechanism. = Book of 500 Puzzles, 1859, prob. 15, pp. 9 & 25.

The Illustrated Boy's Own Treasury. 1860. Practical Puzzles, No. 44: Puzzle purse, pp. 403 & 442‑443. Identical to The Sociable.

Peck & Snyder. 1886.

P. 246: No. 161 _ A magical "pouch".

P. 247: No. 168 _ Grandfather's purse.

Both are shown in Slocum's Compendium.

Hoffmann. 1893. Chap. II, no. 42: Puzzle purse, pp. 43 & 68. This is Ozanam's prob. 32 and finally made it clear to me how it worked.

Burnett Fallow. How to make the "B.O.P." puzzle purse. The Boy's Own Paper 16 (No. 771) (21 Oct 1893) 43-45. As in Ozanam's no. 32.

Davenport's catalogue, op. cit. in 10.T, c1940, p. 3. Tantalizing pants. They are based on a trick stitch. Described as the very latest novelty. Remnants of this stock, made in Japan, are still available from Davenport's as Puzzle pants.

11.H. REMOVING WAISTCOAT WITHOUT REMOVING COAT

Philip Breslaw (attrib.). Breslaw's Last Legacy. 1784? Op. cit. in 6.AF. 1795: 128-129: 'To pull off any Person's Shirt, without undressing him, or having Occasion for a Confederate.'

Manuel des Sorciers. 1825. Pp. 132-133, art. 9: Enlever la chemise à quelqu'un sans le déshabiller.

The Boy's Own Book. 1828: 362. To pull off a person's shirt without undressing him.

Magician's Own Book (UK version). 1871. To take a man's vest off without removing his coat, pp. 239-240. The fact that this English book uses the American term 'vest' makes me suspect this is taken from a US source.

Cassell's. 1881. P. 95: To take a man's waistcoat off without removing his coat. = Manson, 1911, pp. 148-149: Waistcoat puzzle.

Devant. Tricks for Everyone. Op. cit. in 4.A.1. 1910. The waistcoat trick, pp. 106-109.

Games and Tricks _ to make the Party "Go". Supplement to "Pearson's Weekly", Nov. 7th, no year indicated [1930s??]. Removing a waistcoat without the coat, p. 7.

Foulsham's New Party Book. Foulsham, London, nd [1950s?]. P. 49: Removing a boy's waistcoat without taking off his coat.

Gardner. MM&M. 1956.

Reversing the vest, pp. 86-87. Reverse a waistcoat (= vest) while the wearer has his hands clasped, whether he is wearing a coat or not. In theory, you don't even need to unbutton the waistcoat.

Removing the vest, p. 87. Remove a waistcoat without removing the coat.

11.H.1. REMOVING LOOP FROM ARM

Family Friend 3 (1850) 341 & 351. Practical puzzle. No. XXII. Loop around arm with hand in waist coat pocket. Remove the loop without moving the hand. Posed in verse. = Magician's Own Book, 1857, prob. 4: The endless string, pp. 267 & 292. = Book of 500 Puzzles, 1859, pp. 81 & 106. = Boy's Own Conjuring Book, 1860, prob. 5, pp. 229 & 255, but this has a different picture. = Illustrated Boy's Own Treasury, 1860, no. 20, pp. 399 & 438, with slightly abbreviated answer.

Magician's Own Book (UK version). 1871. The string without an end, pp. 204-205. Only shows a loop of string and the problem is a bit unclearly set. Solution is similar to Family Friend.

J. F. Orrin. Easy Magic for Evening Parties. Op. cit. in 7.Q.2. 1930s?? Another magic release (no. 4), pp. 30-31.

McKay. Party Night. 1940. Removing the string, pp. 147-148. As in Family Friend. Notes that many people will fail to do it because they put their hand in their trousers pocket!

Gardner. MM&M. 1956. The puzzling loop, p. 86 & fig. 41 on p. 90. Coat off, loop around arm with hand in waistcoat pocket. Loop must be big enough to pass round his chest.

11.I. HEART AND BALL PUZZLE AND OTHER LOOP PUZZLES

The Alliance or Victoria puzzle has two boards, each with two holes, and a length of string with a largish loop at each end. To disentangle, a loop has to be worked along the string and taken around the entire board at the other end (or, equivalently, around the first board). One can also use a large single loop of string. There are also versions with three holes in each board.

The Heart and Ball puzzle has a heart-shaped piece with several holes in it and a loop of string which goes through the holes and then loops around itself. The other end of the loop has a ball on both strings of the loop and a large knot to prevent it coming free. One has to work the first end of the loop along the string until it comes out along the free end of the loop when it can be passed around the free end and worked back to release the entire string and hence the ball. A simple version of this has just three holes in a straight line on a board and is often sold with the Alliance puzzle.

The Board and Ball puzzle has two holes in a board. A string goes through both holes, crosses itself and then each end comes back through its hole and is terminated with a bead and a knot. A largish bead is located on one of the loops through the holes. To remove, this loop is put through the other hole and passed over the end and brought back, which allows everything to come apart. The alternate approach to the Solomon's Seal described at 11.D is a variant of this approach. See: Family Friend; Magician's Own Book; Anon: Social ....

The Chinese Ladder has several crossbars with holes and a long string winding through the holes and through intermediate discs, with a needle attached to the end of the string. One threads the needle back through all the holes, keeping the end of the loop from pulling through, then threads back through all the ladder holes, avoiding all the disc holes and again keeping the loop from pulling through. When completed, pulling the end causes all the discs to fall off, but the string is still in its original place on the ladder. Making another pass through the discs but not the holes has the effect that when you pull the string free, all the discs are on it. See: Adams & Co.; Hoffmann; Benson; Slocum, Compendium, c1890; Williams; Collins.

Pacioli. De Viribus. c1500. Ff. 206r - 206v, Part 2, Capitulo C: De cavare una stecca de un filo per 3 fori (To remove a stick from a cord through 3 holes). On f. 206r is a marginal drawing clearly showing the string through three holes in one stick.

Cardan. De Rerum Varietate. 1557, ??NYS. = Opera Omnia, vol. III, pp. 245-246. Liber XIII. Ludicrum primum & Ludicrum secondum. The first is the Alliance or Victoria puzzle, with one diagram showing it apart. Second is the version with three holes in each piece, with one diagram, again showing it apart.

Prévost. Clever and Pleasant Inventions. (1584), 1998.

Pp. 133-134. Alliance Puzzle with two holes in each board.

Pp. 134-136. Alliance Puzzle with three holes in each board.

Schwenter. 1636. Part 10, exercise 29, pp. 410-411. Two hole version.

John Wecker. Op. cit. in 7.L.3. 1660. Book XVIII _ Of the Secrets of Sports: The first Pastime and the second Pastime, p. 338. Taken from and attributed to Cardan, with the same diagrams. (I don't know if this material appeared in the 1582 ed.??)

Witgeest. Het Natuurlyk Tover-Boek. 1686. Prob. 44, pp. 35-36 is a two hole version taken from Schwenter.

Ozanam. 1725. Vol. IV, prob. 31, p. 435 & fig. 37, plate 11 (13). This is like the Alliance puzzle in Hoffmann, below.

Alberti. 1747. Art. 31, pp. 205-206 (108‑109) & fig. 38, plate X, opp. p. 206 (between pp. 108 & 109). Taken from Ozanam.

Catel. Kunst-Cabinet. 1790. Das Scheibenspiel, p. 15 & fig. 23 on plate I. The Alliance puzzle, looking much like one of Ozanam's figures.

Bestelmeier. 1801. Item 291: Die verschlungenen Bretchen. Alliance puzzle. The diagram is very obscure and the description is too brief to be certain, but I now see it is copied from part of Catel's text, so this is definitely the Alliance.

Boy's Own Book. The heart and ball puzzle. 1828: 424; 1828‑2: 428; 1829 (US): 220; 1855: 574‑575; 1868: 675-676. = Wehman, New Book of 200 Puzzles, 1908, p. 18.

Nuts to Crack II (1833), no. 91. The heart and ball puzzle. Almost identical to Boy's Own Book.

Crambrook. 1843. P. 4, no. 9: Heart and Ball Puzzle. Check??

Boy's Treasury. 1844. Puzzles and paradoxes, engraved heading of the section, p. 424, shows the puzzle.

Family Friend 3 (1850) 300 & 331. Practical puzzle, No. XX. Drawing shows the artist didn't understand the puzzle at all. = Magician's Own Book, 1857, prob. 16: The heart puzzle, pp. 271-272 & 295. = Book of 500 Puzzles, 1859, pp. 85-86 & 109. = Boy's Own Conjuring Book, 1860, prob. 15, pp. 233 & 258.

Family Friend (Dec 1858) 359. Practical puzzles _ 3. Board and ball, but no name given to it.

Illustrated Boy's Own Treasury. 1860.

Prob. 36, pp. 401‑402 & 441. Identical to Family Friend, 1850, but omitting some comments in the problem.

Prob. 45, pp. 403 & 443. Identical to Family Friend, 1858, with slightly more detailed text.

Adams & Co., Boston. Advertisement in The Holiday Journal of Parlor Plays and Pastimes, Fall 1868. Details?? _ xerox sent by Slocum. P. 6: Chinese Ladder Puzzle. Made of ivory and silk. Ornamentally carved. Probably the same as Hoffmann 17, below _ ??

Magician's Own Book (UK version). 1871.

The puzzle of Cupid: Variation. _ With beads or balls, pp. 227-228. Board and ball puzzle.

The heart puzzle, pp. 228-229. Diagram as in Family Friend, but text is different.

The board and rings, pp. 230-231. A version of the Alliance puzzle. It uses boards with screw-eyes in each end rather than holes and uses a long single loop of string.

Hoffmann. 1893. Chap. II.

No. 11: The heart puzzle, pp. 26 & 52‑53. Photo in Hordern, p. 20.

No. 12: The Alliance (otherwise known as the Victoria) puzzle, pp. 26‑27 & 53. Photo in Hordern, p. 21.

No. 14: The Ariel puzzle, pp. 28 & 54. Photo in Hordern, p. 23.

No. 15: The pen and wheel, pp. 28‑29 & 54.

No. 17: The Chinese ladder, pp. 30 & 55‑56. "It is said to be a genuine importation from China."

At the end of the book (p. 396) is an advertisement for J. Bland's Magical Palace, showing a heart puzzle, an Imperial scale (11.F), Chinese rings (7.M.1) and handcuff puzzle (11.K).

A. Murray. Some simple puzzles. The Boy's Own Paper 17 or 18?? (1894??) 46. Well drawn.

Benson. 1904.

The heart puzzle, p. 210. (= Hoffmann, p. 26.)

The pen and wheel puzzle, pp. 210‑211. (= Hoffmann, pp. 28-29.)

The Alliance puzzle, p. 215. (= Hoffmann, p. 26.)

The Chinese ladder puzzle, p. 216. (= Hoffmann, p. 30.)

Slocum. Compendium. Shows Chinese ladder from Joseph Bland catalogue, c1890, and heart and string puzzle from Johnson Smith 1929 catalogue.

Williams. Home Entertainments. 1914. Another string and buttons puzzle, pp. 112-114. Chinese ladder. Get all the buttons out of the ladder and onto the thread.

"Toymaker". The New-century Cross Puzzle. Work, No. 1394 (4 Dec 1915) 158 (or 153??). Like half of a Victoria or Alliance Puzzle with two holes in the arms of a cross.

"Toymaker". The "Wheel of Fate" Puzzle. Work, No. 1467, (28 Apr 1917) no page number on the xerox from Slocum _ ?? (= Hoffmann, pp. 28-29.)

Collins. Book of Puzzles. 1927.

Pp. 24-26: The Egyptian heart. Heart and ball form.

Pp. 27-29: The Chinese ladder puzzle. Description is a bit cryptic, but he winds up with the string only partly on the ladder and all the discs together on the string.

11.J. MÖBIUS STRIP

Lorraine L. Larison. The Möbius band in Roman mosaics. Amer. Scientist 61 (1973) 544‑547. Describes and illustrates a Roman mosaic in the Museum of Pagan Art, Arles, France, which has a band with five twists. No date given.

At the Möbius Conference at Oxford, in 1990. it was stated that the strip appears in Listing's notes for 1858, apparently a few months before it appears in Möbius's notes.

Walter Purkert. Die Mathematik an der Universität Leipzig von ihrer Gründung bis zum zweiten Drittel des 19. Jahrhunderts. In: H. Beckert & H. Schumann, eds.; 100 Jahre Mathematisches Seminar der Karl‑Marx‑Universität Leipzig; VEB Deutscher Verlag der Wissenschaften, Berlin, 1981; pp. 9‑39. On p. 31, he says that Möbius's Nachlass shows that he discovered the strip in 1858.

J. B. Listing. Der Census räumlicher Complexe. Abh. der Ges. der Wiss. zu Göttingen 10 (1861) 97-180. This appeared as a separate book in 1862. ??NYS _ cited by M. Kline, p. 1164.

A. F. Möbius. Über die Bestimmung des Inhaltes eines Polyeders. Königlich Sächsischen Ges. der Wiss. zu Leipzig 17 (1865) 31-68. = Gesammelte Werke, Leipzig, 1885-1887, vol. 2, pp. 473-512. ??NYS _ cited by M. Kline, p. 1165. He also considers multitwisted bands.

Tissandier. Récréations Scientifiques. 5th ed., 1888, Les anneaux de papier, pp. 272-273. Illustration by Poyet. Shows and describes rings with 0, 1, 2 twists. Not in 2nd ed., 1881. I didn't see whether this was in the 1883 ed.

= Popular Scientific Recreations; [c1890]; Supplement: The paper rings, pp. 867‑869.

Gardner, MM&M, 1956, p. 70 says the earliest magic version he has found is the "1882 enlarged edition of" Tissandier. This may be Popular Scientific Recreations, but I don't see any date in it and the Supplement contains material that was not in the 1883 French ed. _ cf. comments in Common References.

P. G. Tait. Listing's Topologie. Philosophical Mag. (5) 17 (No. 103) (Jan 1884) 30‑46 & plate opp. p. 80. This is based on Listing's Vorstudien zur Topologie (1847) and Der Census räumlicher Complexe (1861). Section 8, pp. 37-38, discusses strips with twists, noting that an odd number of half-twists gives one side and one edge. If the odd number m of half-twists is greater than 1, then cutting it down the middle gives a knotted band with 2m half-twists. He says this was the basis of a pamphlet which was popular in Vienna a few years ago, which showed how to tie a knot in a closed loop.

Anon. [presumably prepared by the editor, Richard A. Proctor]. Trick with paper bands. Knowledge 11 (Jan 1888) 67-68. Short description, based on La Nature, i.e. Tissandier, with copy of the illustration, omitting Poyet's name.

J. B. Bartlett. A glimpse of the "Fourth Dimension". The Boy's Own Paper 12 (No. 588) (19 Apr 1890) 462. Simple description.

Tom Tit, vol. 3. 1893. See entry in 6.Q for a singly-twisted band.

Lewis Carroll. Sylvie and Bruno Concluded. Macmillan, 1893. Chap. 7, pp. 96‑112, esp., pp. 99‑105. Discusses Möbius band ("puzzle of the Paper Ring") and Klein bottle.

Lucas. L'Arithmétique Amusante. 1895. Note IV: Section II: No. 3: Les hélices paradromes, pp. 222-223. Attributes the ideas to Listing's Vorstudien zur Topologie, 1848. Says this is the basis of a lengthy memoir sold at Vienna some years ago showing how one can make a knot in a closed loop _ cf Tait. Gives basic results, including cutting in half.

Herr Meyer. Puzzles. The Boy's Own Paper 19 (No. 937) (26 Dec 1896) 206. No. 3: Paper ring puzzle. Asks what happens when you cut into halves or thirds after one or two or more twists.

Somerville Gibney. So simple! The hexagon, the enlarged ring, and the handcuffs. The Boy's Own Paper 20 (No. 1012) (4 Jun 1898) 573-574. Cuts Möbius band in half twice, then does the same with doubly twisted band.

Hoffmann. Later Magic. (Routledge, London, 1903); Dover, NY, 1979. The Afghan bands, pp. 471‑473. Cuts various strips in half.

Gardner, MM&M, 1956, p. 71, says this is the first usage of the name Afghan Bands that he has found.

C. H. Bullivant. The Drawing Room Entertainer. C. Arthur Pearson, London, 1903. Paper rings, p. 48. Cuts various rings in half.

Dudeney. Cutting-out paper puzzles. Cassell's Magazine ?? (Dec 1909) 187-191 & 233-235. Calls it "paradromic ring" and says it is due to Listing, 1847. Probably based on Lucas.

Devant. Tricks for Everyone. Op. cit. in 4.A.1. 1910. Curious paper patterns, pp. 20-21. Cutting rings with 0, 1, 2 half-twists in half.

Anon. [H. W. R.] Games and Amusements. Ward, Lock & Co., London, nd [c1910??]. The mysterious paper bands, p. 128. Describes bands with 1, 2, 3 twists and cutting them in half.

Williams. Home Entertainments. 1914. The magic paper rings, pp. 104-106. Rings with 0, 1, 2 half-twists to be cut down the middle. Good diagram.

Lee de Forest. US Patent 1,442,682 _ Endless Sound Record and Mechanism Therefor. Filed 5 Oct 1920; patented 16 Jan 1923. 3pp + 2pp diagrams. No references and no mention of any previous forms.

William Hazlett Upson. A. Botts and the Moebius strip. Saturday Evening Post (?? 1945). Reprinted in: Clifton Fadiman, ed.; Fantasia Mathematica; Simon & Schuster, NY, 1958; pp. 155-170.

Owen H. Harris. US Patent 2,479,929 _ Abrasive Belt. Applied 19 Mar 1949; patented 23 Aug 1949. 2pp + 1p diagrams. Same comments as on de Forest.

William Hazlett Upson. Paul Bunyan versus the conveyor belt. ??, 1949. Reprinted in: Clifton Fadiman, ed.; The Mathematical Magpie; Simon & Schuster, NY, 1962; pp. 33‑35.

Gardner. MM&M. 1956. The Afghan Bands, pp. 70-73 & figs. 9-14, pp. 74-77. Describes several usages as a magic effect. Cites Tissandier and Hoffman, cf. above.

James O. Trinkle. US Patent 2,784,834 _ Conveyor for Hot Material. Applied 22 Jul 1952; patented 12 Mar 1957. 2pp + 1p diagrams. Same comments as on de Forest, except that 5 references are mentioned in the file, but not in the patent itself.

James W. Jacobs. US Patent 3,302,795 _ Self-cleaning Filter. Filed 30 Aug 1963; patented 7 Feb 1967. 2pp + 2pp diagrams. "This invention relates to dry cleaning apparatus and more particularly to a self-cleaning filter element comprised of an endless belt having a half twist therein." The diagram does not show the twist very clearly. Same comments as on de Forest, except that the Examiner cites three patents.

Making resistors with math. Time (25 Sep 1964) 49. Richard L. Davis of Sandia Laboratories has made a Möbius strip noninductive resistor. This has metal foil on both sides of a nonconductive Möbius strip with connections opposite to one another. The current flows equally both ways and passes through itself. He found the inductance as low as he had hoped, but he is not entirely clear why it works! Gardner, below, describes this and also cites Electronics Illustrated (Nov 1969) 76f, ??NYS.

Jean J. Pedersen. Dressing up mathematics. MTr 60 (Feb 1968) 118-122. Describes garments with two sides and one edge or one side and one edge or two sides and no edges!!

Gardner. The Möbius strip. SA (Dec 1968) = Magic Show, chap. 9. Describes the above mentioned patents and inventions and numerous stories and works of art using the idea.

Ross H. Casey. US Patent 4,161,270 _ Continuous loop stuffer cartridge having improved Moebius loop tensioning system. Filed 15 Jul 1977; patented 17 Jul 1979. 2pp + 3pp diagrams. This is actually only for an improvement in the idea. "Typically, a cubically-shaped wire form or a plurality of guides are used to effect a Moebius twist in the continuous loop. The invemtion includes an improved Moebius loop device and tensioner in the form of an easily constructed planar triangular-shaped device to effect a Moebius twist and tensioning in a continuous loop." Basically the loop folds around three edges of a triangle. Cites several earlier patents, but Joe Malkevich says none of them relate to the Möbius idea.

In the early 1990s, Tim Rowett found a German making a stainless steel strip with a double twist in it which could be manoeuvred into a double Möbius strip which appeared to be cut in half through the thickness of the strip and which sprang apart when released. In fact it can also be seen as the result of an ordinary cutting of a Möbius strip in half. I cannot recall seeing this behaviour described anywhere, though I imagine it is well known. The process is shown clearly in the following.

Jean-Pierre Petit. Gémellité Cosmique. Text for the month of Juin. Mathematical Calendar: Tous les mois sont maths! for 1990 produced by Editions du Choix, Bréançon, 1989.

Scot Morris. The Next Book of Omni Games. Op. cit. in 7.E. 1991. Pp. 53-54 describes Jacobs' 1963 patent. He says that David M. Walba and colleagues at Univ. of Colorado have synthesised "the first molecular Möbius strip", a molecule called trisTHYME and that they have managed to cut it down the middle!!

11.K. WIRE PUZZLES

Wire and string puzzles are difficult to describe. Only a few were illustrated before 1900. S&B, p. 90, says they first appeared in the 1880s, though some are older _ see 7.M.1, 7.M.5, 11.A, 11.C, 11.D, 11.F, 11.I, 11.K.7 and possibly 11.B, 11.E, 11.H. Ch'ung-En Yü's Ingenious Ring Puzzle Book (op. cit. in 7.M.1) implies that wire and ring puzzles, besides the Chinese Rings, were popular in the Sung Dynasty (960-1279) but I have no confirmation of this assertion. See the entry under Stewart Culin in 7.M.1 for a vague reference to Japanese ring puzzles called Chiye No Wa. This section will cover the various later versions, but without trying to describe them in detail. I have separated the Horseshoes and the Caught Heart, as they are so common.

Wire puzzles were included in general puzzle boxes by 1893 _ see the ad at the end of Hoffmann mentioned in 11.I. By 1912, they were being sold in boxes of just wire puzzles. Six boxes of wire puzzles are offered in Bartl's c1920 Zauberkatalog, p. 305. Wire puzzles are a major component of the Western Puzzle Works, 1926 Catalogue.

See S&B, pp. 88‑115.

Peck & Snyder. 1886. P. 245, No. A _ The puzzle brain links. 11 interlocked links. Not in Slocum's Compendium.

Slocum. Compendium. Shows Egyptian Mystery from Joseph Bland's catalogue, c1890.

Herr Meyer. An improved ring puzzle. In: Hutchison; op. cit. in 5.A; 1891; chap. 70, section III, pp. 573‑574. Folding ring on loop on loop on loop on bar.

Hoffmann. 1893. Chap. VIII: Wire puzzles, pp. 302‑314.

No. 1: The united hearts. (Isomorphic to 11.B.)

No. 2: The triangle.

No. 3: The snake and ring (= Ring and spring puzzle). Cf 11.K.1.

No. 4: The hieroglyph.

No. 5: The interlaced triangles.

No. 6: The double bow and ring (= Horsehoes puzzle).

No. 7: The Egyptian mystery.

No. 8: The ball and spiral.

No. 9: The Unionist puzzle.

No. 10: The Eastern question (= Intertwined question marks = Double witch key).

No. 11: The handcuff puzzle (four interlocked broken rings).

No. 12: The Stanley puzzle.

See also the J. Bland ad on p. 396.

H. F. Hobden. Wire puzzles and how to make them. The Boy's Own Paper 19 (No. 945) (13 Feb 1896) 332-333.

Gridiron and tongs (similar to Hoffmann no. 2).

Hourglass and ring (= Horseshoes = Hoffmann no. 6).

Cupid's bow (similar to Hoffmann no. 1).

Saltspoon and eggwhisk (= Hoffmann no. 8).

Magic rings (= Chinese rings) with 10 rings, requiring 681 moves. (I think it should be 682.)

Slocum. Compendium. Shows one puzzle (Chilian Puzzle) from a set in Montgomery Ward catalogue, 1903.

Benson. 1904. Chap. VIII: Wire puzzles, pp. 236‑240.

The interlaced ring puzzle. (= Hoffmann no. 11.)

The two hearts. (= Hoffmann no. 1.) (Isomorphic to 11.B.)

The bow and ring puzzle. (= Hoffmann no. 6.)

The two crooks. (= Hoffmann no. 10.)

The "X" puzzle. (= Hoffmann no. 7.)

The spiral and ring. (= Hoffmann no. 3.) Cf 11.K.1.

The triangular maze. (= Hoffmann no. 2.)

The ball puzzle. (= Hoffmann no. 8.)

The mysterious loop. (= Hoffmann no. 4.)

Adams. Indoor Games. 1912. Pp. 337‑341.

The gridiron and tongs. (c= Hoffmann no. 2.)

The hourglass and ring. (= Hoffmann no. 6 = horseshoes puzzle.)

Cupid's bow. (c= Hoffmann no. 1.) (Isomorphic to 11.B.)

The saltspoon and eggwhisk. (= Hoffmann no. 8.)

The magic rings. (= Chinese rings, 7.M.1.)

The heart and link. (= Cupid's bow, c= Hoffmann no. 1.) (Isomorphic to 11.B.)

The gridiron and shovel (c= Cupid's bow, c= Hoffmann no. 1.) (Isomorphic to 11.B.)

The double gridiron.

The cross and double links.

The tandem and luggage.

The double link. (= Loony Loop or Satan's Rings.) See 7.M.5. This has a loop of string and is isomorphic to the Chinese rings, 7.M.1.

Bartl. c1920. Vexier- und Geduldspiele, pp. 305-312, shows 43 wire puzzles.

Western Puzzle Works, 1926 Catalogue. Shows about 65 wire puzzles.

Collins. Book of Puzzles. 1927. Some good metal puzzles, pp. 52-53. Shows: The devil's ring; The teaser; The three-in-one rings; The link and rings; The union puzzle. Pp. 44-54 cover other wire puzzles: The Twin Hearts (= Hoffmann no. 1, 11.K.8); The eternal triangle (= Hoffmann no. 2); The bead and spiral (= Hoffmann no. 8); The snake and ring (= Hoffmann no. 3, 11.K.1); The great seven-ring puzzle (= Chinese rings, 7.M.1); The eastern question (= Hoffmann no. 10, Double witch key, 11.K.6).

Ch'ung-En Yü. Ingenious Ring Puzzle Book. 1958. Op. cit. in 7.M.1.

Pp. 18-19 discusses the 'horseshoes puzzle' which is called 'Jade Interlocked Ring Puzzle' and is "the simplest and easiest puzzle of the Incomplete Ring Type". Yü then discusses more complex versions of the puzzle.

P. 21 shows the interlocked nails puzzle.

P. 26 shows a single heart, similar to Hoffmann 1, but with a doubled second part, called Recessed Handle Ring Puzzle. (Isomorphic to 11.B.)

Richard I. Hess. Compendium of Over 7000 Wire Puzzles. 5th ed., published by the author, Rancho Palos Verdes, Mar 1991, 259pp. 7090 wire, entanglement and cast iron puzzles classified in 17 categories. There is an 53 page index and then 205 pages of reduced xeroxes of the actual puzzles. The pictures come out almost as good as drawings. Some of the more obvious combinations do not have pictures. The naming of the puzzles has a certain poetry about it. A118: Type 2 trapeze with baffle, horseshoes, lock and 1-ring key. A226: Cascaded double compound trapeze with baffled heart. B053: Hong Kong house with semicircles (Hard 2-story). C226: Bug (3-ring) with triple cross. D105: Triple Finnish diddle. (Previous editions: 2nd ed, 1982, c500 puzzles; 3rd ed, 1985, c1400 puzzles; 4th ed, 1988, c2600 puzzles.)

11.K.1. RING AND SPRING PUZZLE

A ring is on a spring with sealed ends.

I have seen this illustrated in Wizard's Guide, a catalogue of magic apparatus by W. J. Judd, 1882. ??NX.

Slocum. Compendium. Shows Universal Pocket Puzzle from Montgomery Ward catalogue of 1886.

Peck & Snyder. 1886. P. 162: Universal pocket puzzle.

Hoffmann. 1893. Chap. VIII, no. 3: The snake and ring (= ring and spring puzzle).

Benson. 1904. Chap. VIII: Wire puzzles, pp. 236‑240. The spiral and ring. (= Hoffmann's no. 3.)

I have seen a French example, called L'anneaux prisonnier, dated 1900-1920.

Slocum. Compendium. Shows many later examples: 1913, 1915, 1915, 1919, etc.

Bartl. c1920.

P. 307, no. 61: Der Ring der Nibelungen.

P. 307, no. 63: Spirale mit Nadel. This has a rod down the middle of the spring.

P. 310, no. 87: Ring mit Kette.

Western Puzzle Works, 1926 Catalogue. No. 9: Down and Out.

Collins. Book of Puzzles. 1927. The snake and ring puzzle, pp. 48-49.

11.K.2. STRING AND SPRING PUZZLE

A loop of string goes through the spring which has a few turns and long tails so the string doesn't come off obviously.

Western Puzzle Works, 1926 Catalogue. No. 1877: Loop and Chain.

Slocum. Compendium. Shows Magic Chain from Johnson Smith 1929 catalogue.

11.K.3. MAGIC CHAIN = TUMBLE RINGS

One holds the two top rings and releases the upper one which appears to drop to the bottom.

A magic chain. The Boy's Own Paper 12 (No. 581) (1 Mar 1890) 351. Good picture by Poyet, so this ought to be in Tissandier or Tom Tit, but I haven't seen it.

Der Gute Kamerad. Kolumbus‑Eier. 1890. ??NYS, but reproduced in Edi Lanners' 1976 edition, translated as: Columbus' Egg; Paddington Press, London, 1978; The magic chain, pp. 176‑177, with good illustration on p. 177 _ an enlargement of Poyet's picture with his name removed.

Bartl. c1920. P. 308, no. 71: Konsilkette.

Western Puzzle Works, 1926 Catalogue.

No. 12: Drop Rings Illusion. 15¢. Picture shows 20 rings.

No. 334: Drop Ring illusion, chain of 35 Rings. 15¢. However the picture shows 26 rings??

Davenport's catalogue, op. cit. in 10.T, c1940, pp. 8 & 29, calls it The Wizard's Chain.

Gardner. SA (Aug 1962). = Unexpected, chap. 13. Calls it "tumble rings". Describes the chain with a good diagram for making your own, but gives no indication of its history.

11.K.4. PUZZLE RINGS

William Jones. Finger-Ring Lore. Chatto & Windus, London, 1877. Pp. 313-321 discusses gemmel or gemmow rings with two or three parts. He cites Herrick _ "a ring of jimmals", quotes Dryden's play Don Sebastian describing a two part ring, describes a three-part jointed ring, describes a two part ring excavated in 1800 (medieval??), describes 'a plain geemel wedding-ring' given by the Prince Regent to Mrs. Fitzherbert, describes the five-link wedding ring of Lady Catherine Gray, illustrates a 15C gemmel ring with a head of Lucretia of the type mentioned in Twelfth Night II.v, illustrates Sir Thomas Gresham's betrothal ring of 1544, describes and illustrates several other examples _ 16C, 13C. On pp. 321-322, he mentions an exhibition of some puzzle rings by Rev. John Beck at a meeting of the Archaeological Institute in Mar 1863. These had 7, 4 and 9 parts.

Dudeney. Great puzzle crazes. Op. cit. in 2. 1904. Says he believes it is of Indian origin.

George Frederick Kunz. Rings for the Finger. J. B. Lippincott, Philadelphia, 1917; reprinted by Dover, NY, 1973 (with the two colour plates done in B&W).

Pp. 218‑233 discusses puzzle rings. The earliest forms were gimmel rings which had two or three parts which could be separated for use at betrothal, with the parts rejoined at the wedding and given to the bride. These are known from the 16C _ e.g. the plate facing p. 219 shows a 16C German example from the BM and Sir Thomas Gresham's betrothal ring (c1540) is similar. P. 219 gives a quote from Dryden's play Don Sebastian which describes a two part ring. The plates opp. pp. 220, 221 & 230 show other examples including a three part one from 17C.

Kunz says "the so‑called 'puzzle ring' ... was derived from the East." The plate facing p. 220 shows examples of a three part ring and the common four part Middle Eastern ring, in gold, from the 17C in the BM.

The plate opp. p. 233 shows a six part gold betrothal ring from the Albert Figdor collection, Vienna. This forms a simple chain of six rings.

Stewart Culin. Korean Games. Op. cit. in 4.B.5. Section XX: Ryou‑Kaik‑Tjyo _ Delay Guest Instrument (Ring Puzzle), pp. 31‑32. Says there are many Japanese ring puzzles, called Chiye No Wa, and shows one which seems to be 10 rings linked in a chain _ possibly the simple type of puzzle ring??

Slocum. Compendium. Shows The Lady's and Gentleman's "Wonderful Ring" from Joseph Bland's catalogue, c1890. This has four parts which form a simple chain. The Compendium also shows Puzzle Ring from Johnson Smith 1929 catalogue, which is the classic Turkish or Middle Eastern four part ring.

11.K.5. RING MAZES

These are plates with holes and perhaps raised sections. An open ring must be removed by working it from hole to hole.

S&B 92 says a version was sold by Hamleys in 1879 and appeared as The Boston In-and-Out Puzzle in 1880-1885 and as The Queen's Jubilee Puzzle in 1887.

Peck & Snyder. 1886. P. 250: no. 188 _ The order of stupids.

Edward Hordern has examples from 1880-1900.

Hoffmann. 1893. Chap. X.

No. 42: The Conjurer's Medal, pp. 353 & 392.

No. 43: The Maze Medal, pp. 353-354 & 392.

Western Puzzle Works, 1926 Catalogue.

No. 52: Spider Web.

No. 123: Boxing the Check. (I'm not certain from the picture that this is a ring maze??)

Dudeney. Great puzzle crazes. Op. cit. in 2. 1904. "... the 'Conjurer's Medal,' that came out some years ago ...." Medal with five holes.

11.K.6. INTERLOCKED NAILS, HOOKS, HORNS, ETC.

I have just added this. The puzzle has two interlocked objects. One type has nails bent around a 270^o twist _ see S&B 96-97. A variation, called Wishbone Puzzle, has longer tails _ see S&B 97. A variation has one of the nails made longer with twists at each end, sometimes called Tangle Twister _ see S&B 96. A variation has two circular bits with tails, sometimes called Double Witch Key _ see S&B 97 & 102. Another type has two S-shaped pieces or two J-shaped pieces (hooks) _ see S&B 95.

Hoffmann. 1893. Chap. VIII, no. 10: The Eastern question, p. 307. Interlocked circular bits with tails = Double witch key.

Burnett Fallow. How to make an ingenious link puzzle. The Boy's Own Paper 16 (No. 777) (2 Dec 1893) 143. = Hoffmann no. 10.

Benson. 1904. Chap. VIII: Wire puzzles, pp. 236‑240. The two crooks. (= Hoffmann no. 10.)

Walter S. Jenkins. US Patent 969,481 _ Puzzle. Filed 16 Mar 1908; patented 6 Sep 1910. 3pp + 1p diagrams. Interlocked nails.

Bartl. c1920.

P. 309, no. 76: Hexen-Schlüssel = Double witch key.

P. 311, no. 91: Wodanschlüssel = Hooks.

P. 311, no. 98. A type of Tangle twister.

P. 311, no. 99. Interlocked nails.

P. 311, no. 100. Double withc key.

Western Puzzle Works, 1926 Catalogue.

No. 10: Link the Link. Two hooks.

No. 102: Nails.

No. 71: Elk Horns. Patented.

No. 1978: [unnamed, circular bits with tails, sometimes called Question Marks or Double Witch Key.]

No. 211: Tantalizer _ like nails but one piece is twisted at both ends.

Collins. Book of Puzzles. 1927. The Eastern question, pp. 53-54. As in Hoffmann, with very similar diagram.

S&B 95 calls the interlocked hooks, Loop the Loop or The Devil's Keys, and shows it, but gives no date. S&B 96-97

Ch'ung-En Yü. Ingenious Ring Puzzle Book. 1958. Op. cit. in 7.M.1. P. 21 shows the interlocked nails puzzle.

11.K.7. HORSESHOES PUZZLE

See S&B 99.

Magician's Own Book (UK version). 1871. The ring and wire-loop puzzle, p. 113. With elongated horseshoe parts.

Hoffmann. 1893. Chap. VIII: Wire puzzles, pp. 302‑314. No. 6: The double bow and ring.

H. F. Hobden. Wire puzzles and how to make them. The Boy's Own Paper 19 (No. 945) (13 Feb 1896) 332-333. Hourglass and ring.

Benson. 1904. Chap. VIII: Wire puzzles, pp. 236‑240. The bow and ring puzzle. (= Hoffmann no. 6.)

Adams. Indoor Games. 1912. Pp. 337‑341. The hourglass and ring. (= Hoffmann 6.)

Bartl. c1920.

P. 307, no. 62: Hufe an einer Kette. Here the horseshoes are joined by bits of chain.

P. 308, no. 66: Vexierlyra. Here the horseshoes are in a 'lyre' shape.

P. 310, no. 88: Hufeisen-Vexierspiel.

Ch'ung-En Yü. Ingenious Ring Puzzle Book. 1958. Op. cit. in 7.M.1. Pp. 18-19 discusses the "horseshoes puzzle" which is called "Jade Interlocked Ring Puzzle" and is "the simplest and easiest puzzle of the Incomplete Ring Type". Yü then discusses more complex versions of the puzzle.

11.K.8. THE CAUGHT HEART

This puzzle is isomorphic to 11.B.

Hoffmann. 1893. Chap. VIII: Wire puzzles, pp. 302‑314. No. 1: The united hearts.

H. F. Hobden. Wire puzzles and how to make them. The Boy's Own Paper 19 (No. 945) (13 Feb 1896) 332-333. Cupid's bow (similar to Hoffmann 1).

Benson. 1904. Chap. VIII: Wire puzzles, pp. 236‑240. The two hearts. (= Hoffmann no. 1.)

Adams. Indoor Games. 1912. Pp. 337‑341.

Cupid's bow. (c= Hoffmann 1.)

The heart and link. (= Cupid's bow, c= Hoffmann 1.)

The gridiron and shovel (c= Cupid's bow, c= Hoffmann 1.)

Bartl. c1920. P. 308, no. 65: Vexierherz.

Collins. Book of Puzzles. 1927. The twin hearts puzzle, pp. 44-45. As in Hoffmann, with similar diagram.

Ch'ung-En Yü. Ingenious Ring Puzzle Book. 1958. Op. cit. in 7.M.1. P. 26 shows a single heart, similar to Hoffmann 1, but with a doubled second part, called Recessed Handle Ring Puzzle.

11.L. JACOB'S LADDER AND OTHER HINGING DEVICES

I am now realising that a number of the objects in 6.D, namely the tetraflexagons and the trick or magic books, are just extended forms of the Jacob's ladder. See also Engel in 6.X. The Chinese wallet has two boards with this kind of hinging so it can open on either side, giving different effects.

Bernardino Luini. "A Boy with a Toy" or "Cherub with a Game of Patience". Proby Collection, Elton Hall, Peterborough, Cambridgeshire. The painting is 15" by 13" (38 cm by 33 cm). Luini was a fairly well known Lombard follower of Leonardo, born c1470 and last known in 1533. I have found no indication of the date of the work, but the middle of his working life is c1510. The figure is reproduced from a book of middling quality: Angela Ottino della Chiesa; Bernardino Luini; Electa Editrice, Milan, 1980, item 59. The painting is described in: G. C. Willimson; Bernardino Luini; George Bell and Sons, London, 1900, pp. 104-105. Williamson says the tapes holding the boards together are red and are apparently holding a straw, but he doesn't seem to recognize the object.

Gustav Pauli. Ausstellung von Gemälden der Lombardischen Schule im Burlington Fine Arts Club London April - Juni 1898. (Schluss). Zeitschrift für bildene Kunst (NF) 10 (1898-1899) 149. The Luini was on display and the author describes the toy as a 'Taschenspielerstückchen', a little juggler's trick _ but recall that juggler was long a synonym for magician _ with two boards which allow one to vanish the straw.

Bernardino Licino (attrib.). "Portrait of a Man with a Puzzle". Picture Gallery, Hampton Court Palace, London, Richmond upon Thames, London. Licinio was a Venetian painter born about 1485 and last known in 1549. The painting is described and illustrated (in B&W) in John Shearman; The Early Italian Pictures in the Collection of Her Majesty The Queen; CUP, 1983, item 141, plate 124. It is very similar to another portrait known to be by Licinio and dated 1524, so this is probably c1524 and hence a bit later than the Luini. Shearman cites the Luini painting and Pauli's notice of it. The description says the binding tapes are red, as in the Luini, and both show something like a straw being trapped in the wallet, which suggests some connection between the two pictures, though it may just be that this toy was then being produced in or imported to North Italy and was customarily made with red tapes. On the toy is an inscription: Carpendo Carperis Ipse (roughly: Snapping snaps the snapper), but Shearman says it definitely appears to be an addition, though its paint is not noticebly newer than the rest of the painting. Shearman says the toy comprises 'three or more rectangles ...', though both paintings clearly show just two pieces. My thanks to Peter Hajek who reported seeing this in an email of 22 May 1998

Prévost. Clever and Pleasant Inventions. (1584), 1998. Pp. 136-140. Chinese wallet.

Schwenter. 1636, Part 15, exercise 27, pp. 551-552. "Ein einmaul zu machen." Chinese wallet. I can't find Einmaul in my dicitionaries.

Witgeest. Het Natuurlyk Tover-Boek. 1686. Prob. 66, pp. 49-50. Chinese wallet.

Leslie Daiken. Children's Toys Throughout the Ages. Spring Books, London, 1963. Plate 6 on p. 24 shows "Hand‑operated game of changing pictures, c. 1850" which clearly shows the "Jacob's ladder" hinging with four parts.

Edward Hordern has an example with four panels from c1854.

Hanky Panky. 1872. The magic pocket-book (Die zwei magichen [sic] Brieftaschen), pp. 270-272. This seems to be a form of this mechanism similar to the Chinese wallet.

H. F. Hobden. Jacob's ladder, and how to make it. The Boy's Own Paper 12 (No. 592) (17 May 1890) 526. Says he doesn't know why it is called Jacob's ladder, but that it has been popular "for a number of years". Suggests at least 7 blocks, preferably 12.

Hutchison. Op. cit. in 5.A. 1891. Chap. 71: Jacob's ladder, and other contrivances. Section I _ Jacob's ladder, pp. 583‑585. Shows it clearly. Suggests use of 12 parts, or at least 7.

Davenport's catalogue, op. cit. in 10.T, c1940, pp. 8 & 21, shows the two part version called The Wonderful Magic Book, now often sold as the Chinese Wallet.

11.M. PUZZLE BOXES

A six piece burr with identical flat notched pieces and no key piece is sometimes assembled by forcing together (perhaps after steaming) to make an unopenable money box. Cf 6.W.5.

Catel. Kunst-Cabinet. 1790. Das Vexierkästchen, p. 21 & fig. 21 on plate I. Figure just shows a box. Text says the cover is "made like a see-saw" and one presses firmly on one side and the other lifts up.

Bestelmeier. 1801. Item 208: Eine Kästchen, welches man ohne das Geheimniss zu wissen nicht öfnen kan.

Crambrook. 1843. P. 3 lists 24 types of Puzzling Boxes. ??

1-4: Brass Boxes with Dial-locks or Clock-faces.

5-6: Common Oblong Snuff Box.

7-8: Flat box-root [sic] Snuff Box.

9: Mahogany double-lidded box.

10: Waterloo Boxes, round reeded.

11: Large Shaving ditto.

12: Tin Pricker Box.

13: Secret Cigar Case, in shape of a book.

14: Larger ditto, for a Case for a Pack of Cards.

15-17: Magic Cigar Case.

18: Japan tinplate Oval Box.

19: Brass Oblong Box.

20-22: Indian Ball Puzzles.

23: French Cube Box.

24: The Puzzling Dice Box.

Peck & Snyder. 1886.

P. 129, no. 8: The deceitful tobacco box.

P. 230, no. 20: The Indian puzzle ball.

P. 230, no. 21: The enchanted tea chest.

P. 231, no. 35: The magic fusee box. (Gravity lock.)

P. 241, no. 122: The Not for Joseph snuff or fusee box.

P. 251, no. 203: The wonderful secret ball.

Hoffmann. 1893. Chap. 2, pp. 20-73, shows several items which could be included here. No. 30: The Psycho Match-box has a gravity lock. No. 31-37 are other match-boxes. No. 38-39 are snuff boxes. No. 40-41 are Puzzle Balls.

James Scott. Chinese puzzles, tricks, and traps. Strand Mag. 20 (No. 120) (Dec 1900) 715‑720. Figure 7 shows an object that looks like a three-piece burr but which is a puzzle box made of cardboard or thin wood. It opens by sliding one stick and then pressing its end, when its sides are seen to be hinged and they flex outward. Figures 8‑10 show an ivory globular trinket casket, which has three orthogonal rods crossing in the centre. These have to be turned and slid in the right order to open the box.

Adams. Indoor Games. 1912. A puzzle matchbox, pp. 260-261. Simply concealed slide.

Cecil Henry Bullivant. Every Boy's Book of Hobbies. T. C. & E. C. Jack, London, nd [c1912].

Pp. 46-51: How to make a school box with secret compartments. Simple chest with false bottom and hidden release.

Pp. 52-55: How to make a puzzle box. Small box with a gravity lock.

Bartl. c1920. P. 306, no. 25 is very similar to Hoffmann's Psycho match-box.

11.N. THREE KNIVES MAKE A SUPPORT

New section. The pattern of interlocking knives involved is also used in basketry, woven fences, latticework, etc. Indeed, if they are beams with notches, this gives frameworks which can roof a space much wider than any available beam, e.g. Wren's ceiling of the Sheldonian Theatre, Oxford.

Cardan. De Subtilitate, Book 17, 1550. = Op. Omnia III, p. 629.

Prévost. Clever and Pleasant Inventions. (1584), 1998. PP. 19-20.

van Etten. 1624. Prob. 6 (6), p. 7 (15‑16). Henrion's 1630 Notte cites Cardan.

Schwenter. 1636. Part 15, exercise 7, pp. 536-537. Three knives.

John Wecker. Op. cit. in 7.L.3. 1660. Book XVIII _ Of the Secrets of Sports: Sticks that mutually support one the other, p. 345. Taken from and attributed to Cardan, with very similar diagram. (I don't know if this material appeared in the 1582 ed.??)

Witgeest. Het Natuurlyk Tover-Boek. 1686. Prob. 74, pp. 56-57. Three pipes shown. Text refers to sticks, etc.

Ozanam. 1694. Prob. 16: 1696: 287-288 & fig. 140, plate 47. Prob. 16 & fig. 35, plate 15, 1708: 364. Prob. 20 & fig. 140, plate 47 (45), 1725: vol. 2, 392-393. Prob. 47 & fig. 50, plate 11, 1778: vol. 2, 87; 1803: vol. 2, 93-94; 1814: vol. 2, 76; Prob. 46, 1840: 235.

Badcock. Philosophical Recreations, or, Winter Amusements. [1820]. P. 15, no. 25 & Frontispiece fig. 2: To place three sticks, or tobacco pipes, upon a table in such a manner, that they may appear to be unsupported by any thing but themselves.

Endless Amusement II. 1826?

Pp. 58-59: To arrange three sticks that shall support each other in the air.

Prob. VI, p. 193. "The annexed figure explains a most ingenious device for forming flat roofs or floors, of pieces of timber, little more than half the length of such roof or floor. This plan is well known to architects; and is particularly mentioned in Plot's Natural History of Oxfordshire. ...."

Boy's Own Book. 1828.

The bridge of knives. 1828: 338; 1828‑2: 346; 1829 (US): 153; 1855: 485; 1868: 620.

The toper's tripod. 1828: 338; 1828‑2: 352; 1829 (US): 159; 1855: 485; 1868: 621.

Nuts to Crack II (1833).

No. 94. The bridge of knives.

No. 95. The toper's tripod.

Julia de Fontenelle. Nouveau Manuel Complet de Physique Amusante ou Nouvelles Récréations Physiques .... Nouvelle Édition, Revue, ..., Par M. F. Malepeyre. Librairie Encyclopédique de Roret, Paris, 1850. P. 408 & fig. 147 on plate 4: Disposer trois batons .... Figure copied from Ozanam, 1725.

Magician's Own Book. 1857.

P. 186: The toper's tripod. Use three pipes to support a pot of ale. = Boy's Own Conjuring Book, 1860, p. 162, with different illustration.

P. 187: The bridge of knives. = Boy's Own Conjuring Book, 1860, p. 163 with redrawn illustration.

Anonymous. Every Little Boy's Book A Complete Cyclopædia of in and outdoor games with and without toys, domestic pets, conjuring, shows, riddles, etc. With two hundred and fifty illustrations. Routledge, London, nd. HPL gives c1850, but the text is clearly derived from Every Boy's Book, whose first edition was 1856. The material here is in the 1856 ed of Every Boy's Book (with J. G. Wood as unnamed editor), not yet entered, and later editions, but with different text and pictures.

P. 339: The tobacco pipe jug stand.

P. 351: Bridge of knives.

Magician's Own Book (UK version). 1871.

To make a seat of three canes, p. 123. Says this can also be done with three knives or "rounders" bats or long pipes (called the Toper's Tripod).

The puzzle bridge, p. 123. Stream 15 or 16 feet across, but none of the available planks is more than 6 feet long. He claims that one can use a four plank version of our problem to make a bridge. See the discussion in 6.BD.

Tissandier. Récréations Scientifiques. 1883? Not in the 2nd ed., 1881. I didn't see if these were in the 3rd ed., 1883. 5th ed., 1888. Illustrations by Poyet.

Poser un verre sur trois bâtons ayant chacun une extrémité en l'air, pp. 42-43. Cites and quotes Ozanam.

La carafe et les trois couteaux, p. 43. The knives are resting on three glasses.

Tissandier. Popular Scientific Recreations; Supplement. 1890? Pp. 798-799. To poise a tumbler upon three sticks, each one of which has one end in the air. The water-bottle and the three knives. = (Beeton's) Boy's Own Magazine 3:6 (Jun 1889) 249-251.

Der Gute Kamerad. Kolumbus‑Eier. 1890. ??NYS, but reproduced in Edi Lanners' 1976 edition, translated as: Columbus' Egg; Paddington Press, London, 1978. Uses Poyet's illustrations.

The balancing goblet, p. 22. c= Tissandier.

The floating carafe, pp. 22-24. c= Tissandier.

Blyth. Match-Stick Magic. 1921.

Three-way bridge, p. 52. Three matchsticks on three teacups or tumblers.

Four-way bridge, pp. 52-53. "rather more stable".

Collins. Book of Puzzles. 1927. The bridge builder's puzzle, pp. 41-42. Three and four match bridges over goblets.

Ripley's Believe It or Not!, 16th series, 1971, unpaginated, next to last page, shows six strips forming the sides of a hexagon and then extending, so each strip goes over, under, over, under, four other strips, forming six versions of the three knife configuration.

11.O. BORROMEAN RINGS

New section.

The Borromean rings occur as part of the coat of arms of the Borromeo family, who are counts of the area north of Milan since the 15C. The Golfo Borromeo and the Borromean Islands are in Lago Maggiore, off the town of Stresa. In the 16 and 17C, the Counts of Borromeo built a baroque palace and gardens on the main island, Isola Bella. The Borromean rings can be seen in many places in the palace and gardens, including the sides of the flower pots! Although the Rings have been described as a symbol of the Trinity, I don't know how they came to be part of the Borromean crest, though the guide book describes some of the other features of the crest. (Thanks to Alan and Philippa Collins for the information and loan of the guide book.) Perhaps the most famous member of the family was San Carlo Borromeo (1538-1584), Archbishop of Milan and a leader of the Counter-Reformation, but he does not seem to have used the rings in his crest.

Birtwistle. Math. Puzzles & Perplexities. 1971.

Ring-ring, pp. 135-136 & 195. Three Borromean rings.

String-ring, pp. 136 & 195. If the rings are loops of string, find other ways to join them so that all three are joined, but no two are. Find a way to extend this to n loops.

11.P. THE LONELY MONK

New section. I know of earlier examples from perhaps the 1950s, but the problem must be much older.

A monk starts at dawn and walks to top of a mountain to meditate. Next day, at dawn, he walks down. Show that he is at some point at the same time that he was there on the previous day. This can be approached in two ways.

Let D be the distance to the top of the mountain and let d(t) be his position at time t on the second day minus his position at time t on the first day. Then d(dawn) = D while d(evening) = -D, so at some time t, we must have d(t) = 0.

Equivalently, draw the graphs of his position at time t on both days. The first day's graph starts at 0 at dawn and goes up to D at evening, while the second day's graph begins at D at dawn and goes down to 0 at evening. The two graphs must cross.

This is an application of either the Intermediate Value Theorem of basic real analysis or of the Jordan Curve Theorem of topology.

Ivan Morris. The Lonely Monk and Other Puzzles. (Probably first published by Bodley Head.) Little, Brown and Co., 1970. (Later combined into the Ivan Morris Puzzle Book, Penguin, 1972.) Prob. 1, pp. 14-15 & 91. Monk leaves his mountaintop retreat to go doen to the village at 5:00 one morning and starts back at 5:00 the next morning. Is there always a place which he is at at the same time each day? A note says the problem is based on an idea of Arthur Koestler.

Yuri B. Chernyak & Robert S. Rose. The Chicken from Minsk. BasicBooks, NY, 1995. Chap. 5, prob. 9: Another triumph of central planning, pp. 43-45 & 129-130. This is a complicated version of the problem. There are two roads from A to B, such that for each point on the first road, there is a point at most 20 m away of the second road. This is verified by sending two cars along the two roads, attached by a 20 m phone line. Is it possible to start trucks of width 22 m simultaneously from A to B on one road and from B to A on the other road? The solution uses a graphical method, plotting the distance from A of the first vehicle going along the first road, versus the distance from A of the second vehicle, going along the second road. If the distance along the longer road is D, the verification cars give a graph starting at (0, 0) and ending at (D, D), while the trucks give a graph starting at (0, D) and going to (D, 0).

11.Q. TURNING AN INNER TUBE INSIDE OUT

New section.

Gardner. SA (Jan 1958) c= 1st Book, Chap. 14: Fallacies. Says that the process was illustrated in SA (Jan 1950) and a New Jersey engineer sent in an inner tube which had been turned inside out. GArdner then describes and illustrates painting rings in both directions, one inside, the other outside so they are interlinked at the beginning. He then draws the inner tube apparently inverted, with the rings unlinked and asks for the resolution of this paradox. The solution is given in the Addendum: "the reversal changes the 'grain,' so to speak, opf the torus. As a result, the two rings exchane places and remain linked." Several readers made examples using parts of socks.

Victor Serebriakoff. (A Second Mensa Puzzle Book. Muller, London, 1985.) Later combined with A Mensa Puzzle Book, 1982, Muller, London, as: The Mensa Puzzle Book, Treasure Press, London, 1991. (I have not seen the earlier version.) Problem P13: The Yonklowitz diamond, pp. 164-166, & answer A22, pp. 237-238. After some preliminaries, he asks three questions.

A) Can you pull an inner tube inside out through a small hole?

B) What is the resulting shape?

C) If you draw circles in the two directions, one inside and one outside so they are linked at the beginning, are they linked at the end?

His answers are: A) yes; B) the result has the same shape; C) the circles become unlinked. The last two are wrong. The shape changes _ effectively the two radii change roles. When this is carefully seen, the two circles are seen to still be linked.

11.R. STRING FIGURES

This topic has a vast literature and I intended to omit it as it is very difficult to summarise. However, I have recently acquired the book of Haddon which is an excellent source, so I have included here just a few books with extensive bibliographies which will lead the reader into the literature. I have just learned of:

International String Figure Association, PO Box 5134, Pasadena, California, 91117, USA. Web: http://members.iquest.net/~webweavers/isfa.htm . They publish Bulletin of the International String Figure Association (formerly without the International). [SA (Jun 1998) 77.]

Child. Girl's Own Book. Cat's Cradle. 1833: 76; 1839, 63; 1842: 57. "It is impossible to describe how this is done; but every little girl will find some friend kind enough to teach her." (I don't recall seeing any other references to the game as early as this. The OED cites 1768, 1823, 1824, 1867, 1887.)

Caroline Furness Jayne. String Figures. Scribner's, 1906, ??NYS. Retitled: String Figures and How to Make Them; Dover, 1962. 97 figures given with instructions; another 134 figures are pictured without instructions. 55 references.

Kathleen Haddon [Mrs. O. H. T. Rishbeth]. Artists in String. String Figures: Their Regional Distribution and Social Significance. Methuen, 1930. Discusses string figures in their cultural setting, describing five cultures and some of their figures. 41 string figures given with instructions, and some variants. P. 149 says "descriptions of over eight hundred figures have been published and many more have been collected." The Appendix on p. 151 gives the numbers of figures classified by type of objects represented and location, with a total of 1605 figures plus 101 tricks. Two bibliographies, totalling 116 items. (An abbreviated version, called String Games for Beginners, containing 28 of the figures and omitting the cultural discussions, was printed by Heffers in 1934 and has been in print since then, recently from John Adams Toys.)

Alex Johnston Abraham. String Figures. Reference Publications, Algonac, Michigan, 1988. 31 figures given with instructions plus a chapter on Cat's Cradle. 156 references.