Sources page biographical material

5.R.6. OCTAGRAM PUZZLE
One has an octagram and seven men. One has to place a man on a vacant point and then slide him to an adjacent vacant point, then do the same with the next man, ..., so as to cover seven of the points. The diagram is just an 8-cycle and is the same as the knight's connections on the 3 x 3 board, so the octagram puzzle is equivalent to the 7 knights problem mentioned in 5.F.1. Further, the 4 knights problem of 5.F.1 has the same 8-cycle, with men at alternate points of it.

Versions with different numbers of points.

5 points: Rohrbough.

7 points: Mittenzwey; Meyer.

9 points: Dudeney.

10 points: Bell & Cornelius; Hoffmann; Cohen; Williams; Toymaker; Rohrbough; Putnam.

13 points: Berkeley & Rowland.
Bell & Cornelius. Board Games Round the World. Op. cit. in 4.B.1. 1988. Pentalpha, p. 15. Says that a pentagram board occurs at Kurna, Egypt, c-1400 and that the solitaire game of Pentalpha is played in Crete. This has 9 men to be placed on the vertices and the intersections of the pentagram. Each man must be placed on a vacant point, then slid ahead two positions along one straight line. The intermediate point may be occupied, but the ending point must be unoccupied. Unfortunately we don't know if the Egyptian board was used for this game.

Pacioli. De Viribus. c1500.

Ff. 112r - 113v. .C(apitolo). LXVIII. D(e). cita ch' a .8. porti ch' cosa convi(e)ne arepararli (Chap. 68. Of a city with 8 gates which admits of division ??). = Peirani 158-160. Octagram puzzle with a complex story about a city with 8 gates and 7 disputing factions to be placed at the gates.

F. IVv. = Peirani 8. The Index gives the above as Problem 83. Problem 82: De .8. donne ch' sonno aun ballo et de .7. giovini quali con loro sa con pagnano (Of 8 ladies who are at a ball and of 7 youths who accompany them).

Schwenter. 1636. Part 2, exercise 36, pp. 149-150. Octagram.

Witgeest. Het Natuurlyk Tover-Boek. 1686. Prob. 4, pp. 224-225. Octagram, taken from Schwenter.

Les Amusemens. 1749. P. xxxiii.

Catel. Kunst-Cabinet. 1790. Das Achteck, pp. 12-13 & fig. 36 on plate II. The rules are not clearly described.

Bestelmeier. 1801. Item 290: Das Achteckspiel. Text copies part of Catel.

Charles Babbage. The Philosophy of Analysis -- unpublished collection of MSS in the BM as Add. MS 37202, c1820. ??NX. See 4.B.1 for more details. Ff. 131-133 are an analysis of the heptagram puzzle.

Rational Recreations. 1824. Feat 34, pp. 161-164. Octagram.

Endless Amusement II. 1826? Prob. 28, pp. 203-204. = New Sphinx, c1840, pp. 137-138.

Nuts to Crack IV (1835), no. 194 -- part of a long section called Tricks upon Travellers.

Family Friend (Dec 1858) 359. Practical puzzles -- 1. I don't have the answer.

The Boy's Own Magazine 3 (1857) 159 & 192. Puzzle of the points.

Illustrated Boy's Own Treasury. 1860. Practical Puzzles No. 6, pp. 396 & 436.

The Secret Out. 1859. To Place Seven Counters upon an Eight-Pointed Star, pp. 373-374.

J. J. Cohen, New York. Star puzzle. Advertising card for Star Soap, Schultz & Co., Zanesville, Ohio, Copyright May 1887. Reproduced in: Bert Hochberg; As advertised Puzzles from the collection of Will Shortz; Games Magazine 17:1 (No. 113) 10-13, on p. 11. Identical to pentalpha - see Bell & Cornelius above.

Berkeley & Rowland. Card Tricks and Puzzles. 1892. Card Puzzles No. IX: The reversi puzzle, pp. 8-10. Version with 13 cards in a circle and one can move ahead by any number of steps. If there are x cards and one moves ahead s steps, then x and s must have no common factor.

Hoffmann. 1893.

Chap. VI, pp. 267-268 & 280-281 = Hoffmann-Hordern, pp. 180-181, with photos.

No. 13. No name. Basic octagram puzzle. Photo on p. 181 shows: The Seven Puzzles, by W. & T. Darton, dated 1806-1811; a Tunbridge ware version dated 1825-1840; and Jeu de Zig Zag, by M. D., Paris, 1891-1900.

No. 14. The "Okto" puzzle, pp. 268 & 281. Here the counters and points are coloured. Photo on p. 181 of The "Okto" Puzzle by McGaw, Stevenson & Orr, Ltd. for John Stewart, dated 1880-1895.

Chap. X, no. 8: Crossette, pp. 337 & 374-375 = Hoffmann-Hordern, pp. 229-230, with photo. 10 counters in a circle. Start anywhere and move ahead three. Photo on p. 230 shows The Mystic Seven, a seven counter version, by the Lord Roberts Workshops, 1914-1920.

Mittenzwey. 1895? Prob. 329, pp. 58 & 106; 1917: 329, pp. 52 & 101. Heptagram.

Dudeney. Problem 58: A wreath puzzle. Tit Bits 33 (6 & 27 Nov 1897) 99 & 153. Complex nonagram puzzle involving moves in either direction and producing the original word again.

Clark. Mental Nuts. 1897, no. 54; 1904, no. 80; 1916, no. 69. A little puzzle. Usual octagram.

Benson. 1904. The eight points puzzle, pp. 250 251. c= Hoffmann, no. 13.

Slocum. Compendium. Shows the "Octo" Star Puzzle from Gamage's 1913 catalogue.

Williams. Home Entertainments. 1914.

Crossette, pp. 115-116. Ten points, advancing three places.

Eight points puzzle, pp. 120-121. Usual octagram.

"Toymaker". Top in Hole Puzzle. Work (23 Dec 1916) 200. 10 holes and one has to move to the third position and reverse the top in that hole.

Blyth. Match-Stick Magic. 1921. Crossing the points, pp. 83-84.

Hummerston. Fun, Mirth & Mystery. 1924.

The sacred seven, Puzzle no. 5, pp. 26 & 173. Octagram puzzle on the outer points of the diagram shown in 5.A.

The four rabbits, Puzzle no. 6, pp. 26 & 173. Using the octagram shown in 5.A, put black counters on locations 1 and 2 and white counters on 7 and 8. The object is to interchange the colours. This is like the 4 knights problem except the corresponding 8-cycle has men at positions 1, 2, 5, 6. He counts a sequence of steps by the same man as a move and hence solves it in 6 moves (comprising 16 steps).

Will Blyth. Money Magic. C. Arthur Pearson, London, 1926. Turning the tails, pp. 66-69. 8 coins in a circle, tails up. Count from a tail four ahead and reverse that coin. Get 7 heads up. Counting four ahead means that if you start at 1, you count 1, 2, 3, 4 and reverse 4.

King. Best 100. 1927. No. 64, pp. 26-27 & 54.

Rohrbough. Puzzle Craft. 1932.

Count 4, p. 6. 10 points on a circle, moving ahead 3. (= Rohrbough; Brain Resters and Testers; c1935, p. 21.)

Star Puzzle, p. 8 (= p. 10 of 1940s?). Consider the pentagram with its internal vertices. First puzzle is Pentalpha. Second is to place a counter and move ahead three positions. The object is to get four counters on the points, which is the same as the pentagram puzzle, moving one position.

Jerome S. Meyer. Fun-to-do. Op. cit. in 5.C. 1948. Prob. 18: Odd man out, pp. 27 & 184. Version with 7 positions in a circle and 6 men where one must place a man and then move him three places ahead.

Putnam. Puzzle Fun. 1978. No. 63: Ten card turnover, pp. 11 & 35. Ten face down cards in a circle. Mark a card, count ahead three and turnover.