5.J.1. MRS PERKINS'S QUILT
This is the problem of cutting a square into smaller squares.
Loyd. Cyclopedia, 1914, pp. 248 & 372, 307 & 380. Cut 3 x 3 into 6 squares: 2 x 2 and 5 1 x 1.
Dudeney. AM. 1917. Prob. 173: Mrs Perkins's quilt, pp. 47 & 180. Same as Loyd's "Patch quilt puzzle" in 5.J.
Dudeney. PCP. 1932. Prob. 117: Square of Squares, pp. 53 & 148 149. = 536, prob. 343, pp. 120 & 324 325. c= "Mrs Perkins's quilt".
N. J. Fine & I. Niven, proposers; F. Herzog, solver. Problem E724 -- Admissible Numbers. AMM 53 (1946) 271 & 54 (1947) 41 42. Cubical version.
J. H. Conway. Mrs Perkins's quilt. Proc. Camb. Phil. Soc. 60 (1964) 363 368.
G. B. Trustrum. Mrs Perkins's quilt. Ibid. 61 (1965) 7 11.
Ripley's Puzzles and Games. 1966. Pp. 16-17, item 7. "Can you divide a square into 6 perfect squares?" Answer as in Loyd.
Nick Lord. Note 72.11: Subdividing hypercubes. MG 72 (No. 459) (Mar 1988) 47 48. Gives an upper bound for impossible numbers in d dimensions.
David Tall. To prove or not to prove. Mathematics Review 1:3 (Jan 1991) 29-32. Tall regularly uses the question as an exercise in problem solving. About ten years earlier, a 14 year old girl pointed out that the problem doesn't clearly rule out rejoining pieces. E.g. by cutting along the diagonals and rejoining, one can make two squares.
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