Sources page biographical material

Staines. I accept it ; the meeting place?

Spendall. Beyond the maze in Tuttle.

This refers to a maze in Tothill Fields, close to Westminster Abbey.

Lewis Carroll. Untitled maze. In: Mischmasch, the last of his youthful MS magazines, with entries from 1855 to 1862. Transcribed version in: The Rectory Umbrella and Mischmasch; Cassell, 1932; Dover, 1971; p. 165 of the Dover ed. John Fisher [The Magic of Lewis Carroll; (Nelson, 1973), Penguin, 1975, pp. 19-20] gives this and another example. Cf Carroll-Wakeling, prob. 35: An amazing maze, pp. 46-47 & 75 and Carroll-Gardner, pp. 80-81 for the Mischmasch example. I don't find the other example elsewhere, but it was for Georgina "Ina" Watson, so probably c1870.

Mittenzwey. 1880. Prob. 281, pp. 50 & 100; 1895?: 310, pp. 53-54 & 102; 1917: 310, pp. 49 & 97. The garden of a French place has a maze with 31 points to see. Find a path past all of them with no repeated edges and no crossings. The pattern is clearly based on the Versailles maze of c1675 mentioned in the Historical Sketch above, but I don't recall the additional feature of no crossings occurring before.

C. Wiener. Ueber eine Aufgabe aus der Geometria situs. Math. Annalen 6 (1873) 29 30. An algorithm for solving a maze. BLW asserts this is very complicated, but it doesn't look too bad.

M. Trémaux. Algorithm. Described in Lucas, RM1, 1891, pp. 47 51. ??check 1882 ed. BLW assert Lucas' description is faulty. Also described in MRE, 1st ed., 1892, pp. 130 131; 3rd ed., 1896, pp. 155-156; 4th ed., 1905, pp. 175-176 is vague; 5th-10th ed., 1911 1922, 183; 11th ed., 1939, pp. 255 256 (taken from Lucas); (12th ed. describes Tarry's algorithm instead) and in Dudeney, AM, p. 135 (= Mazes, and how to thread them, Strand Mag. 37 (No. 220) (Apr 1909) 442 448, esp. 446 447).

G. Tarry. Le problème des labyrinthes. Nouv. Annales de Math. (3) 4 (1895) 187 190. ??NYR

Collins. Book of Puzzles. 1927. How to thread any maze, pp. 122-124. Discusses right hand rule and its failure, then Trémaux's method.

M. R. Boothroyd & J. H. Conway. Problems drive, 1959. Eureka 22 (Oct 1959) 15-17 & 22-23. No. 2. 5 x 5 x 5 cubical maze. Get from a corner to an antipodal corner in a minimal number of steps.

Anneke Treep. Mazes... How to get out! (part I). CFF 37 (Jun 1995) 18-21. Based on her MSc thesis at Univ. of Twente. Notes that there has been very little systematic study. Surveys the algorithms of Tarry, Trémaux, Rosenstiehl. Rosenstiehl is greedy on new edges, Trémaux is greedy on new nodes and Trémaux is a hybrid of these. ??-oops-check. Studies probabilities of various routes and the expected traversal time. When the maze graph is a tree, the methods are equivalent and the expected traversal time is the number of edges.

Bernhard Wiezorke. Puzzles und Brainteasers. OR News, Ausgabe 13 (Nov 2001) 52-54. This reports his discovery of a hedge maze in Germany -- the first he knew of. It is in Altjessnitz, near Dessau in Sachsen-Anhalt. (My atlas doesn't show such a place, but Jessnitz is about 10km south of Dessau.) This maze dates from 1720 and has 12 components, with the goal completely separated from the outside so that the 'hand on wall' rule does not solve it. Torsten Silke later told Wiezorke of two other hedge mazes in Germany. One, in Probststeierhagen, Schleswig-Holstein, about 12km NE of Kiel, is in the grounds of the restaurant Zum Irrgarten (At the Labyrinth) and is an early 20C copy of the Altjessnitz example. The other, in Kleinwelka, Sachsen, about 50km NE of Dresden, was made in 1992 and is private. Though it has 17 components, the 'hand on wall' method will solve it. He gives plans of both mazes. He discusses the Seven Bridges of Königsberg, giving a B&W print of the 1641 plan of the city mentioned at the beginning of Section 5.E -- he has sent me a colour version of it. He also describes Tremaux's solution method.