6.BO. BUTTERFLY PROBLEM
I have generally avoided classical geometry of this sort, but Bankoff's paper deserves inclusion.
Leon Bankoff. The metamorphosis of the butterfly problem. MM 60 (1987) 195 210. Includes historical survey of different proofs. The name first appears in the title of the solution of Problem E571, AMM 51 (1944) 91 (??NYS). The problem first occurs in The Gentlemen's Diary (1815) 39 40 (??NYS).
6.BP. EARLY MATCHSTICK PUZZLES
There are too many matchstick puzzles to try to catalogue. Some of them occur in other sections, e.g. 6.AO.1. Here I only include a few very early other examples. At first I thought these would date from mid to late 19C when matches first started to become available, but the earliest examples refer to slips of paper or wood. The earliest mention of matches is in 1858.
Rational Recreations. 1824. Exer. 23, p. 132. Double a sheep pen by adding just two hurdles. I have just realised this is a kind of matchstick puzzle and I suspect there are other early examples of this. It is a little different than most matchstick puzzles in that one is usually not given an initial pattern, but must figure it out. (A hurdle is a kind of panel woven from sticks or reeds used by shepherds to make temporary pens.)
Family Friend 2 (1850) 148 & 179. Practical Puzzle -- No. V. = Illustrated Boy's Own Treasury, 1860, Prob. 46, pp. 404 & 443. "Cut seventeen slips of paper or wood of equal lengths, and place them on a table, to form six squares, as in the diagram. ...."
Magician's Own Book. 1857. Prob. 20: Three square puzzle, pp. 273 & 296. (I had 87 & 110 ??) Almost identical to Family Friend, with a few changes in wording and a different drawing, e.g. "Cut seventeen slips of cardboard of equal lengths, and place them on a table to form six squares, as in the diagram. ...."
The Sociable. 1858. Prob. 2: The magic square, pp. 286 & 301. "With seventeen pieces of wood (lucifer matches will answer the purpose, but be careful to remove the combustible ends, and see that they are all of the same length) make the following figure: [a 2 x 3 array of squares]", then remove 5 matches to leave three squares.
Book of 500 Puzzles. 1859.
Prob. 2: The magic square, pp. 4 & 19. As in The Sociable.
Prob. 20: Three square puzzle, pp. 87 & 110. Identical to Magician's Own Book.
Boy's Own Conjuring Book. 1860. Three-square puzzle, pp. 235 & 259. Identical to Magician's Own Book.
Elliott. Within Doors. Op. cit. in 6.V. 1872. Chap. 1, no. 5: The three squares, pp. 28 & 31. Almost identical to Magician's Own Book, prob. 20, with a slightly different diagram.
Mittenzwey. 1880. Prob. 156-171, 202-212, 240, 242, pp. 32-33, 37-38, 44 & 83-85, 90, 94; 1895?: 179-196, 227-237, 269, 271, pp. 37-38, 41-42, 48 & 85-87, 92, 96; 1917: 179 196, 227-237, 269, 271, pp. 33-34, 38-39, 44 & 82-84, 88, 92. This is the first puzzle book to have lots of matchstick problems, though he doesn't yet use the name, calling them 'Hölzchen' (= sticks). Several problems occur elsewhere, e.g. in 6.AO.1. The last problem is the same as in Jackson.
Sophus Tromholt. Streichholzspiele. Otto Spamer, Leipzig, 1889; 5th ed., 1892; 14th ed., Leipzig, 1909; slightly revised and with a Preface by Rüdiger Thiele, Zentralantiquariat der DDR, Leipzig, 1986; Hugendubel, 1986. [Christopher 1017 is Spamer, 1890. C&B give 1890. There is an edition by Ullstein, Frankfurt, 1990.] This is the earliest book I know which is entirely devoted to matchstick puzzles.
Gaston Tissandier. Jeux et Jouets du jeune age Choix de récréations amusantes & instructives. Ill. by Albert Tissandier. G. Masson, Paris, nd [c1890]. P. 40, no. 4-5: Le problème des allumettes. Make five squares with nine matches. Solution has four small squares and one large one.
Clark. Mental Nuts. 1897, no. 56. The toothpicks. Use 12 toothpicks to make a 2 x 2 array of squares. Move three picks to form three squares.
H. D. Northrop. Popular Pastimes. 1901. No. 1: The magic square, pp. 65 & 71. = The Sociable.
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