Sources page biographical material

6.AE. 6" HOLE THROUGH SPHERE LEAVES CONSTANT VOLUME
Hamnet Holditch. Geometrical theorem. Quarterly J. of Pure and Applied Math. 2 (1858) ??NYS, described by Broman. If a chord of a closed curve, of constant length a+b, be divided into two parts of lengths a, b respectively, the difference between the areas of the closed curve, and of the locus of the dividing point as the chord moves around the curve, will be πab. When the closed curve is a circle and a = b, then this is the two dimensional version given by Jones, below. A letter from Broman says he has found Holditch's theorem cited in 1888, 1906, 1975 and 1976.

Richard Guy (letter of 27 Feb 1985) recalls this problem from his schooldays, which would be late 1920s-early 1930s, and thought it should occur in calculus texts of that time, but could not find it in Lamb or Caunt.

Samuel I. Jones. Mathematical Nuts. 1932. P. 86. ??NYS. Cited by Gardner, (SA, Nov 1957) = 1st Book, chap. 12, prob. 7. Gardner says Jones, p. 93, also gives the two dimensional version: If the longest line that can be drawn in an annulus is 6" long, what is the area of the annulus?

L. Lines. Solid Geometry. Macmillan, London, 1935; Dover, 1965. P. 101, Example 8W3: "A napkin ring is in the form of a sphere pierced by a cylindrical hole. Prove that its volume is the same as that of a sphere with diameter equal to the length of the hole." Solution is given, but there is no indication that it is new or recent.

L. A. Graham. Ingenious Mathematical Problems and Methods. Dover, 1959. Prob. 34: Hole in a sphere, pp. 23 & 145 147. [The material in this book appeared in Graham's company magazine from about 1940, but no dates are provided in the book. (??can date be found out.)]

M. H. Greenblatt. Mathematical Entertainments, op. cit. in 6.U.2, 1965. Volume of a modified bowling ball, pp. 104 105.

C. W. Trigg. Op. cit. in 5.Q. 1967. Quickie 217: Hole in sphere, pp. 59 & 178 179. Gives an argument based on surface tension to see that the ring surface remains spherical as the hole changes radius. Problem has a 10" hole.

Andrew Jarvis. Note 3235: A boring problem. MG 53 (No. 385) (Oct 1969) 298 299. He calls it "a standard problem" and says it is usually solved with a triple integral (??!!). He gives the standard proof using Cavalieri's principle.

Birtwistle. Math. Puzzles & Perplexities. 1971.

Tangential chord, pp. 71-73. 10" chord in an annulus. What is the area of the annulus? Does traditionally and then by letting inner radius be zero.

The hole in the sphere, pp. 87-88 & 177-178. Bore a hole through a sphere so the remaining piece has half the volume of the sphere. The radius of the hole is approx. .61 of the radius of the sphere.

Another hole, pp. 89, 178 & 192. 6" hole cut out of sphere. What is the volume of the remainder? Refers to the tangential chord problem.

Arne Broman. Holditch's theorem: An introductory problem. Lecture at ICM, Helsinki, Aug 1978. Broman then sent out copies of his lecture notes and a supplementary letter on 30 Aug 1978. He discusses Holditch's proof (see above) and more careful modern versions of it. His letter gives some other citations.
6.AF. WHAT COLOUR WAS THE BEAR?
A hunter goes 100 mi south, 100 mi east and 100 mi north and finds himself where he started. He then shoots a bear -- what colour was the bear?

Square versions: Perelman; Klamkin, Breault & Schwarz; Kakinuma, Barwell & Collins; Singmaster.

I include other polar problems here. See also 10.K for related geographical problems.
"A Lover of the Mathematics." A Mathematical Miscellany in Four Parts. 2nd ed., S. Fuller, Dublin, 1735. The First Part is: An Essay towards the Probable Solution of the Forty five Surprising PARADOXES, in GORDON's Geography, so the following must have appeared in Gordon. Part I, no. 10, p. 9. "There is a particular Place of the Earth where the Winds (tho' frequently veering round the Compas) do always blow from the North Point."

Philip Breslaw (attrib.). Breslaw's Last Legacy; or the Magical Companion: containing all that is Curious, Pleasing, Entertaining and Comical; selected From the most celebrated Masters of Deception: As well with Slight of Hand, As with Mathematical Inventions. Wherein is displayed The Mode and Manner of deceiving the Eye; as practised by those celebrated Masters of Mirthful Deceptions. Including the various Exhibitions of those wonderful Artists, Breslaw, Sieur, Comus, Jonas, &c. Also the Interpretation of Dreams, Signification of Moles, Palmestry, &c. The whole forming A Book of real Knowledge in the Art of Conjuration. (T. Moore, London, 1784, 120pp.) With an accurate Description of the Method how to make The Air Balloon, and inject the Inflammable Air. (2nd ed., T. Moore, London, 1784, 132pp; 5th ed., W. Lane, London, 1791, 132pp.) A New Edition, with great Additions and Improvements. (W. Lane, London, 1795, 144pp.) Facsimile from the copy in the Byron Walker Collection, with added Introduction, etc., Stevens Magic Emporium, Wichita, Kansas, 1997. [This was first published in 1784, after Breslaw's death, so it is unlikely that he had anything to do with the book. There were versions in 1784, 1791, 1792, 1793, 1794, 1795, 1800, 1806, c1809, c1810, 1811, 1824. Hall, BCB 39-43, 46-51. Toole Stott 120-131, 966 967. Heyl 35-41. This book went through many variations of subtitle and contents -- the above is the largest version.]. I will cite the date as 1784?.

Geographical Paradoxes.

Paradox I, p. 35. Where is it noon every half hour? Answer: At the North Pole in Summer, when the sun is due south all day long, so it is noon every moment!

Paradox II, p. 36. Where can the sun and the full moon rise at the same time in the same direction? Answer: "Under the North Pole, the sun and the full moon, both decreasing in south declination, may rise in the equinoxial points at the same time; and under the North Pole, there is no other point of compass but south." I think this means at the North Pole at the equinox.

Carlile. Collection. 1793. Prob. CXVI, p. 69. Where does the wind always blow from the north?

Jackson. Rational Amusement. 1821. Geographical Paradoxes.

No. 7, pp. 36 & 103. Where do all winds blow from the north?

No. 8, pp. 36 & 110. Two places 100 miles apart, and the travelling directions are to go 50 miles north and 50 miles south.

Mr. X [cf 4.A.1]. His Pages. The Royal Magazine 10:3 (Jul 1903) 246-247. A safe catch. Airship starts at the North Pole, goes south for seven days, then west for seven days. Which way must it go to get back to its starting point? No solution given.

Pearson. 1907.

Part II, no. 21: By the compass, pp. 18 & 190. Start at North Pole and go 20 miles southwest. What direction gets back to the Pole the quickest? Answer notes that it is hard to go southwest from the Pole!

Part II, no. 15: Ask "Where's the north?" -- Pope, pp. 117 & 194. Start 1200 miles from the North Pole and go 20 mph due north by the compass. How long will it take to get to the Pole? Answer is that you never get there -- you get to the North Magnetic Pole.

Ackermann. 1925. P. 116. Man at North Pole goes 20 miles south and 30 miles west. How far, and in what direction, is he from the Pole?

Richard Guy (letter of 27 Feb 1985) recalls this problem (I think he is referring to the 'What colour was the bear' version) from his schooldays in the 1920s.

H. Phillips. Week End. 1932. Prob. 8, pp. 12 & 188. = his Playtime Omnibus, 1933, prob. 10: Popoff, pp. 54 & 237. House with four sides facing south.

H. Phillips. The Playtime Omnibus. Faber & Faber, London, 1933. Section XVI, prob. 11: Polar conundrum, pp. 51 & 234. Start at the North Pole, go 40 miles South, then 30 miles West. How far are you from the Pole. Answer: "Forty miles. (NOT thirty, as one is tempted to suggest.)" Thirty appears to be a slip for fifty??

Perelman. FFF. 1934. 1957: prob. 6, pp. 14-15 & 19-20: A dirigible's flight; 1979: prob. 7, pp. 18-19 & 25-27: A helicopter's flight. MCBF: prob. 7, pp. 18-19 & 25-26: A helicopter's flight. Dirigible/helicopter starts at Leningrad and goes 500km N, 500km  E, 500km S, 500km W. Where does it land? Cf Klamkin et seq., below.

Phillips. Brush. 1936. Prob. A.1: A stroll at the pole, pp. 1 & 73. Eskimo living at North Pole goes 3 mi south and 4 mi east. How far is he from home?

Haldeman-Julius. 1937. No. 51: North Pole problem, pp. 8 & 23. Airplane starts at North Pole, goes 30 miles south, then 40 miles west. How far is he from the Pole?

J. R. Evans. The Junior Week End Book. Gollancz, London, 1939. Prob. 9, pp. 262 & 268. House with four sides facing south.

Leopold. At Ease! 1943. A helluva question!, pp. 10 & 196. Hunter goes 10 mi south, 10 mi west, shoots a bear and drags it 10 mi back to his starting point. What colour was the bear? Says the only geographic answer is the North Pole.

E. P. Northrop. Riddles in Mathematics. 1944. 1944: 5-6; 1945: 5-6; 1961: 15 16. He starts with the house which faces south on all sides. Then he has a hunter that sees a bear 100 yards east. The hunter runs 100 yards north and shoots south at the bear -- what colour .... He then gives the three sided walk version, but doesn't specify the solution.

E. J. Moulton. A speed test question; a problem in geography. AMM 51 (1944) 216 & 220. Discusses all solutions of the three-sided walk problem.

W. A. Bagley. Puzzle Pie. Op. cit. in 5.D.5. 1944. No. 50: A fine outlook, pp. 54-55. House facing south on all sides used by an artist painting bears!

Leeming. 1946. Chap. 3, prob. 32: What color was the bear?, pp. 33 & 160. Man walks 10 miles south, then 10 miles west, where he shoots a bear. He drags it 10 miles north to his base. What color .... He gives only one solution.

Darwin A. Hindman. Handbook of Indoor Games & Contests. (Prentice Hall, 1955); Nicholas Kaye, London, 1957. Chap. 16, prob. 4: The bear hunter, pp. 256 & 261. Hunter surprises bear. Hunter runs 200 yards north, bear runs 200 yards east, hunter fires south at bear. What colour ....

Murray S. Klamkin, proposer; D. A. Breault & Benjamin L. Schwarz, solvers. Problem 369. MM 32 (1958/59) 220 & 33 (1959/60) 110 & 226 228. Explorer goes 100 miles north, then east, then south, then west, and is back at his starting point. Breault gives only the obvious solution. Schwartz gives all solutions, but not explicitly. Cf Perelman, 1934.

Benjamin L. Schwartz. What color was the bear?. MM 34 (1960) 1-4. ??NYS -- described by Gardner, SA (May 1966) = Carnival, chap. 17. Considers the problem where the hunter looks south and sees a bear 100 yards away. The bear goes 100 yards east and the hunter shoots it by aiming due south. This gives two extra types of solution.

Ripley's Puzzles and Games. 1966. Pp. 18, item 5. 50 mi N, 1000 mi W, 10 mi S to return to your starting point. Answer only gives the South Pole, ignoring the infinitely many cases near the North Pole. Looking at this made me realise that when the sideways distance is larger than the circumference of the parallel at that distance from the pole, then there are other solutions that start near the pole. Here there are three solutions where one starts at distances 109.2, 29.6 or 3.05 miles from the South Pole, circling it 1, 2 or 3 times.

Yasuo Kakinuma, proposer; Brian Barwell and Craig H. Collins, solvers. Problem 1212 -- Variation of the polar bear problem. JRM 15:3 (1982 83) 222 & 16:3 (1983-84) 226 228. Square problem going one mile south, east, north, west. Barwell gets the explicit quadratic equation, but then approximates its solutions. Collins assumes the earth is flat near the pole.

David Singmaster. Bear hunting problems. Submitted to MM, 1986. Finds explicit solutions for the general version of Perelman/Klamkin's problem. [In fact, I was ignorant of (or had long forgotten) the above when I remembered and solved the problem. My thanks to an editor (Paul Bateman ??check) for referring me to Klamkin. The Kakinuma et al then turned up also.] Analysis of the solutions leads to some variations, including the following.

David Singmaster. Home is the hunter. Man heads north, goes ten miles, has lunch, heads north, goes ten miles and finds himself where he started.

Used as: Explorer's problem by Keith Devlin in his Micromaths Column; The Guardian (18 Jun 1987) 16 & (2 Jul 1987) 16.

Used by me as one of: Spring term puzzles; South Bank Polytechnic Computer Services Department Newsletter (Spring 1989) unpaged [p. 15].

Used by Will Shortz in his National Public Radio program 6? Jan 1991.

Used as: A walk on the wild side, Games 15:2 (No. 104) (Aug 1991) 57 & 40.

Used as: The hunting game, Focus 3 (Feb 1993) 77 & 98.

Used in my Puzzle Box column, G&P, No. 11 (Feb 1995) 19 & No. 12 (Mar 1995) 41.

Bob Stanton. The explorers. Games Magazine 17:1 (No. 113) (Feb 1993) 61 & 43. Two explorers set out and go 500 miles in each direction. Madge goes N, W, S, E, while Ellen goes E, S, W, N. At the end, they meet at the same point. However, this is not at their starting point. How come? and how far are they from their starting point, and in what direction? They are not near either pole.

Yuri B. Chernyak & Robert S. Rose. The Chicken from Minsk. BasicBooks, NY, 1995. Chap. 11, prob. 9: What color was that bear? (A lesson in non-Euclidean geometry), pp. 97 & 185-191. Camper walks south 2 km, then west 5 km, then north 2 km; how far is he from his starting point? Solution analyses this and related problems, finding that the distance x satisfies 0  x  7.183, noting that there are many minimal cases near the south pole and if one is between them, one gets a local maximum, so one has to determine one's position very carefully.

David Singmaster. Symmetry saves the solution. IN: Alfred S. Posamentier & Wolfgang Schulz, eds.; The Art of Problem Solving: A Resource for the Mathematics Teacher; Corwin Press, NY, 1996, pp. 273-286. Sketches the explicit solution to Klamkin's problem as an example of the use of symmetric variables to obtain a solution.

Anonymous. Brainteaser B163 -- Shady matters. Quantum 6:3 (Jan/Feb 1996) 15 & 48. Is there anywhere on earth where one's shadow has the same length all day long?
6.AG. MOVING AROUND A CORNER
There are several versions of this. The simplest is moving a ladder or board around a corner -- here the problem is two-dimensional and the ladder is thin enough to be considered as a line. There are slight variations -- the corner can be at a T or + junction; the widths of the corridors may differ; the angle may not be a right angle; etc. If the object being moved is thicker -- e.g. a table -- then the problem gets harder. If one can use the third dimension, it gets even harder.
H. E. Licks. Op. cit. in 5.A, 1917. Art. 110, p. 89. Stick going into a circular shaft in the ceiling. Gets [h^2/3 + d^2/3)]^3/2 for maximum length, where h is the height of the room and d is the diameter of the shaft. "A simple way to solve a problem which has proved a stumbling block to many."

Abraham. 1933. Prob. 82 -- Another ladder, pp. 37 & 45 (23 & 117). Ladder to go from one street to another, of different widths.

E. H. Johnson, proposer; W. B. Carver, solver. Problem E436. AMM 47 (1940) 569 & 48 (1941) 271 273. Table going through a doorway. Obtains 6th order equation.

J. S. Madachy. Turning corners. RMM 5 (Oct 1961) 37, 6 (Dec 1961) 61 & 8 (Apr 1962) 56. In 5, he asks for the greatest length of board which can be moved around a corner, assuming both corridors have the same width, that the board is thick and that vertical movement is allowed. In 6, he gives a numerical answer for his original values and asserts the maximal length for planar movement, with corridors of width w and plank of thickness t, is 2 (w2   t). In vol. 8, he says no two solutions have been the same.

L. Moser, proposer; M. Goldberg and J. Sebastian, solvers. Problem 66 11 -- Moving furniture through a hallway. SIAM Review 8 (1966) 381 382 & 11 (1969) 75 78 & 12 (1970) 582 586. "What is the largest area region which can be moved through a "hallway" of width one (see Fig. 1)?" The figure shows that he wants to move around a rectangular corner joining two hallways of width one. Sebastian (1970) studies the problem for moving an arc.

J. M. Hammersley. On the enfeeblement of mathematical skills .... Bull. Inst. Math. Appl. 4 (1968) 66 85. Appendix IV -- Problems, pp. 83 85, prob. 8, p. 84. Two corridors of width 1 at a corner. Show the largest object one can move around it has area < 2 2 and that there is an object of area  π/2 + 2/π = 2.2074.

Partial solution by T. A. Westwell, ibid. 5 (1969) 80, with editorial comment thereon on pp. 80 81.

T. J. Fletcher. Easy ways of going round the bend. MG 57 (No. 399) (Feb 1973) 16 22. Gives five methods for the ladder problem with corridors of different widths.

Neal R. Wagner. The sofa problem. AMM 83 (1976) 188 189. "What is the region of largest area which can be moved around a right angled corner in a corridor of width one?" Survey.

R. K. Guy. Monthly research problems, 1969 77. AMM 84 (1977) 807 815. P. 811 reports improvements on the sofa problem.

J. S. Madachy & R. R. Rowe. Problem 242 -- Turning table. JRM 9 (1976 77) 219 221.

G. P. Henderson, proposer; M. Goldberg, solver; M. S. Klamkin, commentator. Problem 427. CM 5 (1979) 77 & 6 (1979) 31 32 & 49 50. Easily finds maximal area of a rectangle going around a corner.

Research news: Conway's sofa problem. Mathematics Review 1:4 (Mar 1991) 5-8 & 32. Reports on Joseph Gerver's almost complete resolution of the problem in 1990. Says Conway asked the problem in the 1960s and that L. Moser is the first to publish it. Says a group at a convexity conference in Copenhagen improved Hammersley's results to 2.2164. Gerver's analysis gives an object made up of 18 segments with area 2.2195. The analysis depends on some unproven general assumptions which seem reasonable and is certainly the unique optimum solution given those assumptions.

A. A. Huntington. More on ladders. M500 145 (Jul 1995) 2-5. Does usual problem, getting a quartic. The finds the shortest ladder. [This turns out to be the same as the longest ladder one can get around a corner from corridors of widths w and h, so 6.AG is related to 6.L.]

6.AH. TETHERED GOAT
A goat is grazing in a circular field and is tethered to a post on the edge. He can reach half of the field. How long is the rope? There are numerous variations obtained by modifying the shape of the field or having buildings within it. In recent years, there has been study of the form where the goat is tethered to a point on a circular silo in a large field -- how much area can he graze?
Upnorensis, proposer; Mr. Heath, solver. Ladies Diary, 1748-49 = T. Leybourn, II: 6-7, quest. 302. [I have a reference to p. 41 of the Ladies' Diary.] Circular pond enclosed by a circular railing of circumference 160 yards. Horse is tethered to a post of the railing by a rope 160 yards long. How much area can he graze?

Dudeney. Problem 67: Two rural puzzles -- No. 67: One acre and a cow. Tit Bits 33 (5 Feb & 5 Mar 1898) 355 & 432. Circular field opening onto a small rectangular paddock with cow tethered to the gate post so that she can graze over one acre. By skilful choice of sizes, he avoids the usual transcendental equation.

Arc. [R. A. Archibald]. Involutes of a circle and a pasturage problem. AMM 28 (1921) 328 329. Cites Ladies Diary and it appears that it deals with a horse outside a circle.

J. Pedoe. Note 1477: An old problem. MG 24 (No. 261) (Oct 1940) 286-287. Finds the relevant area by integrating in polar coordinates centred on the post.

A. J. Booth. Note 1561: On Note 1477. MG 25 (No. 267) (Dec 1941) 309 310. Goat tethered to a point on the perimeter of a circle which can graze over ½, ⅓, ¼ of the area.

Howard P. Dinesman. Superior Mathematical Puzzles. Op. cit. in 5.B.1. 1968.

No. 8: "Don't fence me in", pp. 87. Equilateral triangular field of area 120. Three goats tethered to the corners with ropes of length equal to the altitude. Consider an area where n goats graze as contributing 1/n to each goat. What area does each goat graze over?

No. 53: Around the silo, pp. 71 & 112-113. Goat tethered to the outside of a silo of diameter 20 by a rope of length 10π, i.e. he can just get to the other side of the silo. How big an area can he graze? The curve is a semicircle together with two involutes of a circle, so the solution uses some calculus.

Marshall Fraser. A tale of two goats. MM 55 (1982) 221 227. Gives examples back to 1894.

Marshall Fraser. Letter: More, old goats. MM 56 (1983) 123. Cites Arc[hibald].

Bull, 1998, below, says this problem has been discussed by the Internet newsgroup sci.math some years previously.

Michael E. Hoffman. The bull and the silo: An application of curvature. AMM 105:1 (Jan 1998) ??NYS -- cited by Bull. Bull is tethered by a rope of length L to a circular silo of radius R. If L  πR, then the grazeable area is L³/3R + πL²/2. This paper considers the problem for general shapes.

John Bull. The bull and the silo. M500 163 (Aug 1998) 1-3. Improves Hoffman's solution for the circular silo by avoiding polar coordinates and using a more appropriate variable, namely the angle between the taut rope and the axis of symmetry.

Keith Drever. Solution 186.5 -- Horse. M550 188 (Oct 2002) 12. A horse is tethered to a point on the perimeter of a circular field of radius 1. He can graze over all but 1/π of the area. How long is the rope? This turns out to make the problem almost trivial -- the rope is 2 long and the angle subtended at the tether is π/2.

6.AI. TRICK JOINTS
S&B, pp. 146 147, show several types.

These are often made in two contrasting woods and appear to be physically impossible. They will come apart if one moves them in the right direction. A few have extra complications. The simplest version is a square cylinder with dovetail joints on each face -- called common square version below. There are also cases where one thinks it should come apart, but the wood has been bent or forced and no longer comes apart -- see also 6.W.5.

See Bogesen in 6.W.2 for a possible early example.

Johannes Cornelus Wilhelmus Pauwels. UK Patent 15,307 -- Improved Means of Joining or Fastening Pieces of Wood or other Material together, Applicable also as a Toy. Applied: 9 Nov 1887; complete specification: 9 Aug 1888; accepted: 26 Oct 1888. 2pp + 1p diagrams. It says Pauwels is a civil engineer of The Hague. Common square version.

Tom Tit, vol. 2. 1892. Assemblage paradoxal, pp. 231-232. = K, no. 155: The paradoxical coupling, pp. 353 354. Common square version with instructions for making it by cutting the corners off a larger square.

Emery Leverett Williams. The double dovetail and blind mortise. SA (25 Apr 1896) 267. The first is a trick T joint.

T. Moore. A puzzle joint and how to make it. The Woodworker 1:8 (May 1902) 172. S&B, p. 147, say this is the earliest reference to the common square version -- but see Pauwels, above. "... the foregoing joint will doubtless be well-known to our professional readers. There are probably many amateur woodworkers to whom it will be a novelty."

Hasluck, Paul N. The Handyman's Book. Cassell, 1903; facsimile by Senate (Tiger Books), Twickenham, London, 1998. Pp. 220 223 shows various joints. Dovetail halved joint with two bevels, p. 222 & figs. 703-705 of pp. 221-222. "... of but little practical value, but interesting as a puzzle joint."

Dudeney. The world's best puzzles. Op. cit. in 2. 1908. Shows the common square version "given to me some ten years ago, but I cannot say who first invented it." He previously published it in a newspaper. ??look in Weekly Dispatch.

Samuel Hicks. Kinks for Handy Men: The dovetail puzzle. Hobbies 31 (No. 790) (3 Dec 1910) 248-249. Usual square dovetail, but he suggests to glue it together!

Dudeney. AM. 1917. Prob. 424: The dovetailed block, pp. 145 & 249. Shows the common square version -- "... given to me some years ago, but I cannot say who first invented it." He previously published it in a newspaper. ??as above

Anon. Woodwork Joints, 1918, op. cit. in 6.W.1. A curious dovetail joint, pp. 193, 195. Common square version. Dovetail puzzle joint, pp. 194 195. A singly mortised T joint, with an unmortised second piece.

E. M. Wyatt. Woodwork puzzles. Industrial Arts Magazine 12 (1923) 326 327. Doubly dovetailed tongue and mortise T joint called 'The double (?) dovetail'.

Sherman M. Turrill. A double dovetail joint. Industrial Arts Magazine 13 (1924) 282 283. A double dovetail right angle joint, but it leaves sloping gaps on the inside which are filled with blocks.

Collins. Book of Puzzles. 1927. Pp. 134 135: The dovetail puzzle. Common square version.

E. M. Wyatt. Puzzles in Wood, 1928, op. cit. in 5.H.1.

The double (?) dovetail, pp. 44 45. Doubly dovetailed tongue and mortise T joint.

The "impossible" dovetail joint, p. 46. Common square version.

Double lock dovetail joint, pp. 47 49. Less acceptable tricks for a corner joint.

Two way fanned half lap joint, pp. 49 50. Corner joint.

A. B. Cutler. Industrial Arts and Vocational Education (Jan 1930). ??NYS. Wyatt, below, cites this for a triple dovetail, but I could not not find it in vols. 1 40.

R. M. Abraham. Prob. 225 -- Dovetail Puzzle. Winter Nights Entertainments. Constable, London, 1932, p. 131. (= Easy to do Entertainments and Diversions with coins, cards, string, paper and matches; Dover, 1961, p. 225.) Common square version.

Abraham. 1933. Prob. 304 -- Hexagon dovetail; Prob. 306 -- The triangular dovetail, pp. 142 143 (100 & 102).

Bernard E. Jones, ed. The Practical Woodworker. Waverley Book Co., London, nd [1940s?]. Vol. 1: Lap and secret dovetail joints, pp. 281 287. This covers various secret joints -- i.e. ones with concealed laps or dovetails. Pp. 286-287 has a subsection: Puzzle dovetail joints. Common square version is shown as fig. 28. A pentagonal analogue is shown as fig. 29, but it uses splitting and regluing to produce a result which cannot be taken apart.

E. M. Wyatt. Wonders in Wood. Bruce Publishing Co., Milwaukee, 1946.

Double double dovetail joint, pp. 26 27. Requires some bending.

Triple dovetail puzzle, pp. 28 29. Uses curved piece with gravity lock.

S&B, p. 146, reproduces the above Wyatt and shows a 1948 example.

W. A. Bagley. Puzzle Pie. Op. cit. in 5.D.5. 1944. Dovetail deceptions, p. 64. Common square version and a tapered T joint.

Allan Boardman. Up and Down Double Dovetail. Shown on p. 147 of S&B. Square version with alternate dovetails in opposite directions. This is impossible!

I have a set of examples which belonged to Tom O'Beirne. There is a common square version and a similar hexagonal version. There is an equilateral triangle version which requires a twist. There is a right triangle version which has to be moved along a space diagonal! [One can adapt the twisting method to n-gons!]

Dick Schnacke (Mountain Craft Shop, American Ridge Road, Route 1, New Martinsville, West Virginia, 26155, USA) makes a variant of the common square version which has two dovetails on each face. I bought one in 1994.