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B.1. LOWERING FROM TOWER PROBLEM



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5.B.1. LOWERING FROM TOWER PROBLEM
The problem is for a collection of people (and objects or animals) to lower themselves from a window using a rope over a pulley, with baskets at each end. The complication is that the baskets cannot contain very different weights, i.e. there is a maximum difference in the weights, otherwise they go too fast. This is often attributed to Carroll.
Carroll-Collingwood. 1899. P. 318 (Collins: 232-233 (232 is lacking in my copy)). = Carroll-Wakeling II, prob. 4: The captive queen, pp. 8 & 65-66. 3 people of weights 195, 165, 90 and a weight of 75, with difference at most 15. He also gives a more complex form. No solutions. Although the text clearly says 165, the prevalence of the exact same problem with 165 replaced by 105 makes me wonder if this was a misprint?? Wakeling says there is no explicit evidence that Carroll invented this, and neither book assigns a date, but Carroll seems a more original source than the following and he was more active before 1890 than after.

An addition is given in both books: add three animals, weighing 60, 45, 30.

Lemon. 1890. The prisoners in the tower, no. 497, pp. 65 & 116. c= Sphinx, The escape, no. 113, pp. 19 & 100 101. Three people of weights 195, 105, 90 with a weight of 75. The difference in weights cannot be more than 15.

Hoffmann. 1893. Chap. IV, no. 28: The captives in the tower, pp. 150 & 196 = Hoffmann Hordern, p. 123. Same as Lemon.

Brandreth Puzzle Book. Brandreth's Pills (The Porous Plaster Co., NY), nd [1895]. P. 3: The captives in the tower. Same as Lemon. Identical to Hoffmann. With colour picture. No solution.

Loyd. The fire escape puzzle. Cyclopedia, 1914, pp. 71 & 348. c= MPSL2, prob. 140, pp. 98 99 & 165. = SLAHP: Saving the family, pp. 59 & 108. Simplified form of Carroll's problem. Man, wife, baby & dog, weighing a total of 390.

Williams. Home Entertainments. 1914. The escaping prisoners, pp. 126-127. Same as Lemon.

Rudin. 1936. No. 92, pp. 31-32 & 94. Same as Lemon.

Haldeman-Julius. 1937. No. 150: Fairy tale, pp. 17 & 28. Same as Lemon, except the largest weight is printed as 196, possibly an error.

Kinnaird. Op. cit. in 1 -- Loyd. 1946. Pp. 388 389 & 394. Same as Lemon.

Simon Dresner. Science World Book of Brain Teasers. Scholastic Book Services, NY, 1962. Prob. 61: Escape from the tower, pp. 29 & 99 100. Same as Lemon.

Robert Harbin [pseud. of Ned Williams]. Party Lines. Oldbourne, London, 1963. Escape, p. 29. As in Lemon.

Howard P. Dinesman. Superior Mathematical Puzzles. Allen & Unwin, London, 1968. No. 60: The tower escape, pp. 78 & 118. Same as Carroll. Answer in 15 stages. He cites Carroll, noting that Carroll did not give a solution and he asks if a shorter solution can be found.

F. Geoffrey Hartswick. In: H. O. Ripley & F. G. Hartswick; Detectograms and Other Puzzles; Scholastic Book Services, NY, 1969. No. 15: Stolen treasure puzzle, pp. 54 55 & 87. Same as Lemon.



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