7. arithmetic & number theoretic recreations a. Fibonacci numbers

Ff. 117v - 118r. .C(apitolo). LXXI. D(e). un quadro quale .3. per ogni verso Diametro elati et giontovi .3. doventa .4. per og' verso (Of a square which has 3 on every diagonal and side and adding 3 has 4 in every direction). Says to start with one object in each cell of a 3 x 3 array, which has three on each line, then add one to the cells along a diagonal to get 4 in each line. This gets 6 on that diagonal however, but he ignores that.

Ff. IVv - Vr. = Peirani 8. The Index gives the above as Problem 88 and continues with the following. Problem 89: De uno abate ch' tolse aguardar certo monasterio de monache in levante contandole sera e matina per ogni verso tante et pur daloro schernito desperato la bandona (Of an abbot who tries to guard a certain monastery of monks in the Levant by counting evening and morning the same on each side and how the sneering desperados abandoned it ??).

van Etten. English ed., 1653, prob. 72: Of the game of square formes, pp. 124 125. 24 men on sides of a fort, becoming 28 and 20. Discusses case of 12 men making 3, 4 or 5 on a side.

Anon. Schau Platz der Betrieger: Entworfen in vielen List  und Lustigen Welt Händeln. Hamburg & Frankfurt, 1687, pp. 543 545. ??NYS (A&N, p. 5.)

Ozanam. 1694. Prob. 1, 1696: 1-2; 1708: 1 2; 1725: 1-3. Prob. 20, 1778: 172-174; 1803: 172-174; 1814: 151-153. Prob. 19, 1840: 77 78. Blind abbess and 24 nuns with 9 on a side. 1696 gives three arrangements with 24, 28, 20 on a side. 1725 adds another arrangement with 32. 1778 says Ozanam has presented this in a rather indecent manner to excite the curiosity of his readers and adds arrangements with 36 and 18 on a side. The last has 5 and 4 in the corners and none in the side cells, but can be done in other ways. 1803 drops the 'indecent' reference.

Dilworth. Schoolmaster's Assistant. 1743. Part IV: Questions: A short Collection of pleasant and diverting Questions, p. 168. Problem 1. General stationing guards around a castle, wanting 18 on a side, starting with 48 men and changing to 56, then 40.

Les Amusemens. 1749. Prob. 11, p. 131: Les rangs de Neuf. Wine merchant with 32 bottles, 9 on a side, reduced to 28, 24, 20.

Catel. Kunst-Cabinet. Vol. 2, 1793. Die Nonnenlist (The nuns' strategem), pp. 15-16 & fig. 251 on plate XII. The diagram shows the eight outside cells with 5 spots in the form of a 5 on a die and one spot in the centre. However, the text says there are 25 cones or pieces and one must read the instructions to learn the game. The number of pieces seems peculiar and I'm not entirely sure this is our problem, despite its name.

Bestelmeier. 1801. Item 191: Die Nonnenlist. Picture is an obscure copy of Catel. Text is copied from part of Catel, but says there are 15 pieces!

Badcock. Philosophical Recreations, or, Winter Amusements. [1820]. Pp. 10-11, no. 20: The blind abbess and her nuns. 9 on a side, starts with 24 and changes to 28, then 20.

Jackson. Rational Amusement. 1821. Arithmetical Puzzles.

No. 22, pp. 6 & 57. 18 men on a side of a castle, total = 48, 56, 40.

No. 29, pp. 7 & 58. Blind abbess and nuns, 9 on a side, total ranging from 20 to 32.

No. 32, pp. 8 & 59. Wine merchant and casks, 9 on a side, total of 32, diminished to 20.

No. 36, pp. 9 & 59-60. Blind abbess and nuns, equal numbers on each side, then with four extras, then with four gone away. Solution starts with 24.

John Badcock. Domestic Amusements, or Philosophical Recreations. Op. cit. in 6.BH. [1823]. Pp. 156-157, no. 194: Dishonest contrivance. 32 sheep, with 12 on a side, reduced to 28.

Rational Recreations. 1824. Exer. 18, pp. 94-95: The convent. 24 increased to 28 then reduced to 20.

Manuel des Sorciers. 1825. Pp. 75-78, art. 38. ??NX Blind abbess. Gets totals of 32, 28, 24, 20.

Endless Amusement II. 1826?

Pp. 108-109: Curious arithmetical question. 9 on each side, changed from a total of 24 to 20, 28, 32.

Prob. 32, pp. 209-210. Uses a novel figure -- take a 3 x 3 square and draw the 1 x 1 cells in each corner, then diagonally connect the interior vertices of these to form an X in the central cell. This gives 8 cells -- the four squares at the corners and four pentagonal shapes along the edges. (See Wehman, p. 22.) 15 on each side, beginning with 40, reduced to 36. = New Sphinx, c1840, p. 139.

The Boy's Own Book. The wine merchant and his clerk. 1828: 412; 1828 2: 418; 1829 (US): 211; 1855: 565; 1868: 669. 32 bottles, reducing to 20.

The Riddler. 1835. The wine merchant and his clerk, pp. 4-5. Identical to Boy's Own Book.

Crambrook. 1843. P. 10, no. 23: The Blind Abbess and her Nuns, a laughable trick.

Magician's Own Book. 1857.

The square of Gotham, pp. 229-230. 24 scholars, 9 on a side, changing to 20, 28, 32. = Boy's Own Conjuring Book.

Prob. 24: The nuns, pp. 274 & 297. 24 nuns. = Book of 500 Puzzles, prob. 24. = Boy's Own Conjuring Book, prob. 23. c= Illustrated Boy's Own Treasury, prob. 29.

Landells. Boy's Own Toy-Maker. 1858. Pp. 149-150. c= Magician's Own Book, prob. 24.

The Sociable. 1858. Prob. 21: The blind abbot and the monks, pp. 292-294 & 309. 24 monks, 9 on a side, changed to 20, 28, 32, 36, 18. = Book of 500 Puzzles, prob. 21.

Book of 500 Puzzles. 1859.

Prob. 21: The blind abbot and the monks, pp. 10-12 & 27. As in The Sociable.

Prob. 24: The nuns, pp. 88 & 111. Identical to Magician's Own Book, prob. 24.

Boy's Own Conjuring book. 1860.

The square of Gotham, pp. 199 200. Identical to Magician's Own Book.

Prob. 23: The nuns, pp. 236 & 261. Identical to Magician's Own Book, prob. 24.

Illustrated Boy's Own Treasury. 1860. Prob. 29, pp. 429 & 434. Very similar to Magician's Own Book, prob. 24.

Vinot. 1860. Art. LVIII: Les étrennes du Commissaire, pp. 75-76. 140 bottles of wine arranged 1, 34, 1 on each side. Clerk steals four bottles sixteen times, reducing to 17, 2, 17.

The Secret Out (UK). c1860. Both of the following are presented with cards.

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