Sources page biographical material

5.J.2. CUBING THE CUBE
S. Chowla. Problem 1779. Math. Student 7 (1939) 80. (Solution given in Brooks, et al., Duke Math. J., op. cit. in 5.J, section 10.4, but they give no reference to a solution in Math. Student.)
5.J.3. TILING A SQUARE OF SIDE 70 WITH SQUARES OF SIDES

1, 2, ..., 24
J. R. Bitner. Use of Macros in Backtrack Programming. M.Sc. Thesis, ref. UIUCDCS R 74 687, Univ. of Illinois, Urbana Champaign, 1974, ??NYS. Shows such a tiling is impossible.
5.K. DERANGEMENTS
Let D(n) = the number of derangements of n things, i.e. permutations leaving no point fixed.
Eberhard Knobloch. Euler and the history of a problem in probability theory. Gaņita-Bhāratī [NOTE: ņ denotes an n with an underdot] (Bull. Ind. Soc. Hist. Math.) 6 (1984) 1 12. Discusses the history, noting that many 19C authors were unaware of Euler's work. There is some ambiguity in his descriptions due to early confusion of n as the number of cards and n as the number of the card on which a match first occurs. Describes numerous others who worked on the problem up to about 1900: De Moivre, Waring, Lambert, Laplace, Cantor, etc.
Pierre Rémond de Montmort. Essai d'analyse sur les jeux de hazards. (1708); Seconde edition revue & augmentee de plusieurs lettres, (Quillau, Paris, 1713 (reprinted by Chelsea, NY, 1980)); 2nd issue, Jombert & Quillau, 1714. Problèmes divers sur le jeu du trieze, pp. 54 64. In the original game, one has a deck of 52 cards and counts 1, 2, ..., 13 as one turns over the cards. If a card of rank i occurs at the i-th count, then the player wins. In general, one simplifies by assuming there are n distinct cards numbered 1, ..., n and one counts 1, ..., n. One can ask for the probability of winning at some time and of winning at the k-th draw. In 1708, Montmort already gives tables of the number of permutations of n cards such that one wins on the k-th draw, for n = 1, ..., 6. He gives various recurrences and the series expression for the probability and (more or less) finds its limit. In the 2nd ed., he gives a proof of the series expression, due to Nicholas Bernoulli, and John Bernoulli says he has found it also. Nicholas' solution covers the general case with repeated cards. [See: F. N. David; Games, Gods and Gambling; Griffin, London, 1962, pp. 144 146 & 157.] (Comtet and David say it is in the 1708 ed. I have seen it on pp. 54-64 of an edition which is uncertain, but probably 1708, ??NX. Knobloch cites 1713, pp. 130-143, but adds that Montmort gave the results without proofs in the 1708 ed. and includes several letters from and to John I and Nicholas I Bernoulli in the 1713 ed., pp. 290-324, and mentions the problem in his Preface -- ??NYS.)

Abraham de Moivre. The Doctrine of Chances: or, A Method of Calculating the Probability of Events in Play. W. Pearson for the Author, London, 1718. Prob. XXV, pp. 59-63. (= 2nd ed, H. Woodfall for the Author, London, 1738. Prob. XXXIV, pp. 95-98.) States and demonstrates the formula for finding the probability of p items to be correct and q items to be incorrect out of n items. One of his examples is the probability of six items being deranged being 53/144.

L. Euler. Calcul de la probabilité dans le jeu de rencontre. Mémoires de l'Académie des Sciences de Berlin (7) (1751(1753)) 255 270. = Opera Omnia (1) 7 (1923) 11 25. Obtains the series for the probability and notes it approaches 1/e.

L. Euler. Fragmenta ex Adversariis Mathematicis Deprompta. MS of 1750 1755. Pp. 287 288: Problema de permutationibus. First published in Opera Omnia (1) 7 (1923) 542 545. Obtains alternating series for D(n).

Ozanam-Montucla. 1778. Prob. 5, 1778: 125-126; 1803: 123-124; 1814: 108-109; 1840: omitted. Describes Jeu du Treize, where a person takes a whole deck and turns up the cards, counting 1, 2, ..., 13 as he goes. He wins if a card of rank i appears at the i th count. Montucla's description is brief and indicates there are several variations of the game. Hutton gives a lengthier description of one version. Cites Montmort for the probability of winning as .632..

L. Euler. Solutio quaestionis curiosae ex doctrina combinationum. (Mem. Acad. Sci. St. Pétersbourg 3 (1809/10(1811)) 57 64.) = Opera Omnia (1) 7 (1923) 435 440. (This was presented to the Acad. on 18 Oct 1779.) Shows D(n) = (n 1) [D(n 1) + D(n 2)] and D(n) = nD(n 1) + ( 1)ⁿ.

Ball. MRE. 1st ed., 1892. Pp. 106-107: The mousetrap and Treize. In the first, one puts out n cards in a circle and counts out. If the count k occurs on the k-th card, the card is removed and one starts again. Says Cayley and Steen have studied this. It looks a bit like a derangement question.

Bill Severn. Packs of Fun. 101 Unusual Things to Do with Playing Cards and To Know about Them. David McKay, NY, 1967. P. 24: Games for One: Up and down. Using a deck of 52 cards, count through 1, 2, ..., 13 four times. You lose if a card of rank i appears when you count i, i.e. you win if the cards are a generalized derangement. Though a natural extension of the problem, I can't recall seeing it treated, perhaps because it seems to get very messy. However, a quick investigation reveals that the probability of such a generalized derangement should approach e^-4.

Brian R. Stonebridge. Derangements of a multiset. Bull. Inst. Math. Appl. 28:3 (Mar 1992) 47-49. Gets a reasonable extension to multisets, i.e. sets with repeated elements.