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6.BB. DOUBLING AN AREA WITHOUT CHANGING ITS HEIGHT OR

WIDTH
The area is usually a square, but other shapes are possible. If one views it as a reduction, one can reduce the area to any fraction of the original!
The Sociable. 1858. Prob. 41: The carpenter puzzled, pp. 298 & 316. 3 x 3 square of wood with holes in it forming a 4 x 4 array with the corner holes at the corners of the board. Claims one can cut 1/4 of the board out of the centre without including any holes. But this only gets 2/9 of the area -- double the central square. = Book of 500 Puzzles, 1859, prob. 41, pp. 16 & 34. = Secret Out, 1859, pp. 386-387.

Indoor & Outdoor. c1859. Part II: prob. 14: The carpenter puzzled, pp. 133 134. Almost identical with The Sociable.

Hanky Panky. 1872. P. 226 shows the same diagram as the solution in The Sociable, but there is no problem or text.

Lewis Carroll. Letter of 15 Mar 1873 to Helen Feilden. = Carroll-Collingwood, pp. 212-215 (Collins 154-155), without solution. Cf Carroll-Wakeling, prob. 28: The square window, pp. 36-37 & 72. Halve the area of a square window. Wakeling and Carroll-Gardner, p. 52, give the surname as Fielden, but it is Feilden in Carroll-Collingwood and in Cohen, who sketches her life. Wakeling writes that Feilden is correct.

Mittenzwey. 1880. Prob. 216-217, pp. 38-39 & 90; 1895?: 241-242, pp. 43 & 92; 1917: 241 242, pp. 39 & 88. Divide a rectangle or square into two pieces with the same height and width as the square. Solution is to draw a diagonal.

Lemon. 1890. A unique window, no. 444, pp. 58 & 114. The philosopher's puzzle, no. 660, pp. 82 & 121.

Don Lemon. Everybody's Scrap Book of Curious Facts. Saxon, London, 1890. P. 82 quotes an article from The New York World describing this as 'an excellent, if an old, puzzle'.

Hoffmann. 1893. Chap. IX, no. 28: A curious window, pp. 319 & 327 = Hoffmann-Hordern, pp. 211-212. Notes that either a diamond or a triangle in appropriate position can be so doubled.

Clark. Mental Nuts. 1897, no. 40. The building lot. "Have a lot 50 x 100. Want to build a house 50 x 100 and have the yard same size. How?" Solution shows 50 x 100 with a diagonal drawn.

Pearson. 1907. Part II, no. 79: At a duck pond, pp. 79 & 176. A square pond is to be doubled without disturbing the duckhouses at its corners.

Wehman. New Book of 200 Puzzles. 1908. The carpenter puzzled, p. 39. = The Sociable.

Will Blyth. Handkerchief Magic. C. Arthur Pearson, London, 1922. Doubling the allotment, pp. 23-24.

Hummerston. Fun, Mirth & Mystery. 1924. Some queer puzzles, Puzzle no. 76, part 6, pp. 164 & 183. Solution notes that a window in the shape of a diamond or a right triangle or an isosceles triangle can be doubled in area without changing its width or height.

King. Best 100. 1927.

No. 2, pp. 7 8 & 38. Same as Indoor & Outdoor, with the same error.

No. 4, pp. 8 & 39. Halve a square window. See Foulsham's.

Foulsham's Games and Puzzles Book. W. Foulsham, London, nd [c1930]. No. 2, pp. 5 & 10. Double a window without changing its height or width. (This is one of the few cases where the problem is not quite identical to King.)

M. Adams. Puzzle Book. 1939. Prob. B.117: Enlarging the allotment, pp. 86 & 110. Double a square allotment without disturbing the trees at the corners.