Sources page biographical material

6.S.2. OTHER SETS OF PIECES
See Hoffmann & S&B, cited at the beginning of 6.S, for general surveys.

See Bailey in 6.AS.1 for an 1858 puzzle with 10 pieces and The Sociable and Book of 500 Puzzles, prob. 10, in 6.AS.1 for an 11 piece puzzle.

There are many versions of this idea available and some are occasionally given in JRM.

The Richter Anchor Stone puzzles and building blocks were inspired by Friedrich Froebel (or Fröbel) (1782 1852), the educational innovator. He was the inventor of Kindergartens, advocated children's play blocks and inspired both the Richter Anchor Stone Puzzles and Milton Bradley. The stone material was invented by Otto Lilienthal (1848 1896) (possibly with his brother Gustav) better known as an aviation pioneer -- they sold the patent and their machines to F. Adolph Richter for 1000 marks. The material might better be described as a kind of fine brick which could be precisely moulded. Richter improved the stone and began production at Rudolstadt, Thüringen, in 1882; the plant closed in 1964. Anchor was the company's trademark. He made at least 36 puzzles and perhaps a dozen sets of building blocks which were popular with children, architects, engineers, etc. The Deutsches Museum in Munich has a whole room devoted to various types of building blocks and materials, including the Anchor blocks. The Speelgoed Museum 'Op Stelten' (Sint Vincentiusstraat 86, NL-4902 (or 4901) GL Oosterhout, Noord-Brabant, The Netherlands; tel: [phone]; fax: [phone]) has a room of Richter blocks and some puzzles. There was an Anker Museum in the Netherlands (Stichting Ankerhaus (= Anker Museum); Opaalstraat 2 4 (or Postf. 1061), NL-2400 BB Alphen aan den Rijn, The Netherlands; tel: [phone]) which produced replacement parts for Anker stone puzzles. Modern facsimiles of the building sets are being produced at Rudolstadt.

In 1996 I noticed the ceiling of the room to the south of the Salon of the Ambassadors in the Alcazar of Seville. This 15C? ceiling was built by workmen influenced by the Moorish tradition and has 112 square wooden panels in a wide variety of rectilineal patterns. One panel has some diagonal lines and looks like it could be used as a 10 piece tangram-like puzzle. Consider a 4 x 4 square. Draw both diagonal lines, then at two adjacent corners, draw two lines making a unit square at these corners. At the other two corners draw one of these two lines, namely the one perpendicular to their common side. This gives six isosceles right triangles of edge 1; two pentagons with three right angles and sides 1, 2, 1, 2, 2; two quadrilaterals with two right angles and sides 2, 1, 2, 22. Since geometric patterns and panelling are common features of Arabic art, I wonder if there are any instances of such patterns being used for a tangram-like puzzle?

Grand Jeu du Casse Tête Français en X. Pieces. ??NYS -- described and partly reproduced in Milano, who says it comes from Paris and dates it 1818? The figures are anthropomorphic and are most similar to those in Jeu du Casse Tete Russe.

Grande Giuocho del Rompicapo Francese. Milano presso Pietro e Giuseppe Vallardi Contrada di S. Margherita N^o 401(? my copy is small and faint). ??NYS -- described and partly reproduced in Milano, who dates it as 1818-1820. Identical problems as in the previous item, but the figures have been redrawn rather than copied exactly.

Allizeau. Les Métamorphoses ou Amusemens Géometriques Dédiée aux Amateurs Par Allizeau. A Paris chex Allizeau Quai Malaquais, N^o 15. ??NYS -- described and partly reproduced in Milano. This uses 15 pieces and the problems tend to be architectural forms, like towers.

Jackson. Rational Amusement. 1821. Geometrical Puzzles, nos. 20-27, pp. 27-29 & 88-89 & plate II, figs. 15-22. This is a set of 20 pieces of 8 shapes used to make a square, a right triangle, three squares, etc.

Crambrook. 1843. P. 4, no. 1: Pythagorean Puzzle, with Book. Though not illustrated, this is probably(??) the puzzle described in Hoffmann, below, which was a Richter Anchor puzzle No. 12 of the same name and is still occasionally seen. See S&B 28.

Edward Hordern's collection has a Circassian Puzzle, c1870, with many pieces, but I didn't record the shapes -- cf Boy's Own Book, 1843 (Paris), in section 6.S.

Mittenzwey. 1880.

Prob. 177-179, pp. 34 & 86; 1895?: 202-204, pp. 38-39 & 88; 1917: 202-204, pp. 35 & 84-85. Consider the ten piece version of dissecting 5 squares to one (6.AS.1). Use the pieces to make:

a squat octagon, a house gable-end, a church (no solution), etc.;

two dissimilar rectangles;

three dissimilar parallelograms, two dissimilar trapezoids. Solution says one can make many other shapes with these pieces, e.g. a trapezoid with parallel sides in the proportion 9 : 11.

Prob. 181-184, pp. 34-35 & 87-88; 1895?: 206-209, pp. 39 & 89-90; 1917: 206-209, pp. 36 & 85-86. Take six equilateral triangles of edge 2. Cut an equilateral triangle of edge 1 from the corner of each of them, giving 12 pieces. Make a hexagon in eight different ways [there are many more -- how many??] and three tangram-like shapes.

Prob. 195-196, pp. 36 & 89; 1895?: 220-221, pp. 41 & 91; 1917: 220-221, pp. 37 & 87. Use four isosceles right triangles, say of leg 1, to make a square, a 1 x 4 rectangle and an isosceles right triangle.

Nicholas Mason. US Patent 232,140 - Geometrical Puzzle-Block. Applied: 13 May 1880; patented 14 Sep 1880. 1p plus 2pp diagrams. Five squares, six units square, each cut into four pieces in the same way. Start at the midpoint of a side and cut to an opposite corner. (This is the same cut used to produce the ten piece 'Five Squares to One' puzzle.) Cut again in the triangle just formed, from the same midpoint to a point one unit from the right angle corner of the piece just made. This gives a right triangle of sides 3, 1, 10 and a triangle of sides 5, 10, 345. Cut again from the same midpoint across the trapezoidal piece made by the first cut, to a point five units from the corner previously cut to. This gives a triangle of sides 5, 35, 210 and a right trapezoid with sides 2,10, 1, 6, 3. This was produced as Hill's American Geometrical Prize Puzzle in England ("Price, One Shilling.") in 1882. Harold Raizer produced a facsimile version, with facsimile box label and instructions for IPP22. The instructions have 20 problems to solve and the solutions have to be submitted by 1 May 1882.

Hoffmann. 1893. Chap. III, no. 3: The Pythagoras Puzzle, pp. 83-85 & 117-118 = Hoffmann Hordern, pp. 69-72. This has 7 pieces and is quite like the Tangram -- see comment under Crambrook. Photo on p. 71, with different version in Hordern Collection, p. 50.

C. Dudley Langford. Note 1538: Tangrams and incommensurables. MG 25 (No. 266) (Oct 1941) 233 235. Gives alternate dissections of the square and some hexagonal dissections.

C. Dudley Langford. Note 2861: A curious dissection of the square. MG 43 (No. 345) (Oct 1959) 198. There are 5 triangles whose angles are multiples of π/8 = 22½^o. He uses these to make a square.

See items at the end of 6.S.