Sources page probability recreations

Part I, no. 25: A family party, pp. 120 & 184. Two widows and sons marry and each couple has a daughter, causing 24 apparent people to be only 6.

Part I, no. 36: Quite a family party, pp. 123 & 186. Same as Hoffmann.

Part I: A table of affinity, p. 127. Reports that M. de Lesseps and his son were to marry sisters and discusses the complications that would ensue.

Mr. X [cf 4.A.1]. His Pages. The Royal Magazine 26:6 (Oct 1911) 569. The mean Duke. Same as Hoffmann.

Henry Edwards Huntington (1850-1927) married Arabella Duval Huntington ( -1924), the widow of his uncle Collis P. Huntington ( -1900) in 1913. Henry and Arabella were the same age.

Dudeney. AM. 1917. Several examples, including the following.

Prob. 52: Queer relationships, pp. 8 & 153. Discusses two brothers who married two sisters. One man and one woman died and the survivors married and had a child. The man married his deceased wife's sister which was legal, so he is married to the woman and his child is legitimate. But the woman married her deceased husband's brother, which was not legal at the time, so she is not married to the man and her child is illegitimate!! Mentions a man who married his widow's sister and a man who has a nephew, but the nephew is not the nephew of his sister.

Prob. 54: A family party, pp. 8 & 153. 23 apparent people are only 7. See Leske.

Prob. 55: A mixed pedigree, pp. 8-9 & 153. A is B's father's brother-in-law, brother's father-in-law and father-in-law's brother.

Prob. 56: Wilson's poser, pp. 9 & 153. A is B's uncle and nephew. This is due to two men marrying the mother of the other and both couples producing -- the results are A and B.

Ahrens. A&N. 1918. Pp. 105 122, esp. 111 122. Describes an 11C report of a person with only three grandparents, but it turns out to be erroneous. However, Cleopatra had only three grandparents, since her parents were half siblings -- I had believed they were full siblings which would give her only two grandparents. See also the 1730 entry about Christopher Burraway.

For convenience in the following, let n parents denote one's ancestors n generations back, so 1 parents are parents, 2 parents are grandparents, 3 parents are great grandparents, etc. Normally one has 2ⁿ n parents.

Prince Don Carlos of Spain (1545 1568) had only 4 3 parents, 6  4 parents, 12  5 parents and 20 6 parents. Ahrens also gives more extended examples, e.g. the 12 generations of ancestors of Kaiser Wilhelm II comprise only 1549 people instead of the expected 8190, and one person occurs in 70 places.

Smith. Number Stories. 1919. Pp. 114 116 & 142. Tartaglia's problem. Also a more complex version where 27 apparent people are only 7.

Ackermann. 1925. Pp. 92 93. Three mothers, each with two daughters, require only 7 beds.

Loyd Jr. SLAHP. 1928. A puzzling estate, pp. 68 & 111. Three fathers and three sons are only four people.

Collins. Fun with Figures. 1928. He was his own grandfather, pp. 231-232. Claims to quote a Pittsburgh newspaper story of a resident who committed suicide when he found he was his own grandfather. Son and father married widow and daughter.

Dr. Th. Wolff. Die lächelnde Sphinx. Academia Verlagsbuchhandlung, Prague, 1937.

Prob. 4, pp. 188 & 197. 'My grandfather is only five years older than my father.'

Prob. 5, pp. 188 & 197. 'My father and my grandfather are twins.'

Haldeman-Julius. 1937. No. 88: Marriage problem, pp. 11 & 25. How can a man have married his widow's sister? (Also entered under Deceased Wife's Sister.)

Depew. Cokesbury Game Book. 1939.

Three ducks, p. 201. Two fathers and two sons make three people.

Separate Room, p. 216. Three mothers, each with two daughters, make seven people.

Joseph Leeming. Riddles, Riddles, Riddles. Franklin Watts, 1953; Fawcett Gold Medal, 1967.

P. 50, no. 5: "If your uncle's sister is not your aunt, just what relation is she to you?

P. 53, no. 32: "If Dick's father is Tom's son, what relation is Dick to Tom?"

P. 91, no. 3: "A doctor had a brother who went out West. But the man who went out West had no brother. How can this be?"

P. 91, no. 4: "Two men, with their two wives and two sons, are related to each other as follows: The men are each other's fathers and sons, their wives' fathers and husbands, and their children's fathers and grandfathers. The women are the children's mothers and sisters; and the boys are uncles to each other. How can this be?" Same as Abbot Albert, prob. 12.

P. 92, no. 8. Schoolteacher and his daughter, the minister's wife and the minister are just three people.

P. 109, no. 11: "Sisters and brothers have I none, but that man's father is my father's son. Who am I looking at?"

P. 113, no. 44: "What relation is that child to its father who is not its father's own son?"

P. 113, no. 47: "Two Indians are standing on a hill, and one is the father of the other's son. What relation are the two Indians to each other?"

P. 153, no. 30: "It wasn't my sister, not my brother, But it still was the child of my father and mother. Who was it?"

Ripley's Believe It Or Not! 6th series, Pocket Books, NY, 1958. P. 145. Jacob van Nissen, of Zwolle, Holland, and his son married a girl and her mother.

W. Leslie Prout. Think Again. Frederick Warne & Co., London, 1958. Catch Quiz, No. 6, pp. 12 & 115. "Said one boy to another: "My mother's sister is your sister's mother." What relation were the two boys?"

Kathleen Rafferty. Dell Pencil Puzzles & Word Games. Dell, NY, 1975. Noodle Nudger 3, pp. 106 & 127. "Mary's husband's father-in-law is Mary's husband's brother's brother-in-law, and Mary's sister-in-law is Mary's brother's stepmother. HOW COME?" "Mary's father married her husband's sister."

Scot Morris. The Book of Strange Facts and Useless Information. Doubleday, NY, 1979, p. 98. In order to give his divorced mother some benefit from his father's estate, Robert Berston adopted his mother in 1967.

Patrick Donovan. Peculiar People. Fontana, 1984. P. 76 reports that Dave Woodhouse of Wolverhampton divorced his wife and married her mother in 1983 at a double wedding where his ex-wife was also married to a new man.

Ripley's Believe It or Not! - Strange Coincidences. Tor (Tom Doherty Associates), NY, 1990, p. 21. George Clark Cheever, of Warsaw, Indiana, three of his sons and one of his daughters all married siblings.

Marcia Ascher. Ethnomathematics. Op. cit. in 4.B.10. 1991. Chapter Three: The logic of kinship relations, pp. 66-83. Gives a number of folk puzzles and references.

Two mothers and two daughters are three people (Brazil).

Two brothers say "My brother's son is buried there"; third brother says "My brother's son is not buried there" (Ireland).

Who is the sister of my aunt, who is not my aunt? (Puerto Rico).

His mother is my mother's mother-in-law (Russia).

Who is my mother's brother's brother-in-law? (Wales).

"Smallweed" diary column. The Guardian (10 Apr 1993) 18. Bill Wyman of the Rolling Stones married and later divorced Mandy Smith. Mandy's mother Patsy is about to marry Stephen Wyman, Bill's son from his first marriage.

Item on front of Society section of The Guardian (2 Apr 1997) 1. "A 46-year-old Bedfordshire woman has married the father of an 18-year-old girl who eloped with her husband."

David Singmaster. Some years before I read a description of some English aristocrat which said that he only had four grandparents while most people had eight. This was later corrected -- he had only four great-grandparents while most people had eight. Of course this puzzled me for a bit and I worked out a reasonable way this could have happened. I later realised that there is another way it could have happened, though I think the second method is slightly less likely. I posed the problem of finding both ways as a Brain Jammer: Four Great-Grandparents; Weekend Telegraph (12 Dec 1998) 21 & (2 Jan 1999) 17. At the time I didn't know of any real examples, but Ahrens (1918) says Prince Don Carlos of Spain (1545 1568) had only four great-grandparents. I also used this on a Puzzle Panel program. When cousins marry, their children have six great-grandparents.

Mindgames. Frontiers (a UK popular science magazine) No. 1 (Spring 1998) 107. "My wife's sister is also her cousin. How can this be?" Solution is that her father married his dead wife's sister and had another daughter.

9.E.1. THAT MAN'S FATHER IS MY FATHER'S SON, ETC.
New section -- I have just found the 17C example, but there must be other and older examples?? But see Proctor, 1883. The problem continues to perplex people -- see Fairon, 1992.

For the 'Blind beggar' type of problem see: Boy's Own Book, 1828; Rowley, 1866; Rowley, 1875; Neil, 1880s; Lemon, 1890; Clark, 1897; Home Book, 1941; Charlot, c1950s. Again one thinks this should be older.

Some of the items given above, could go in here.
Tomé Pinheiro da Veiga. Fastiginia o fastos geniales. (This work is a chronicle of courtly life in Castilla, from 1601 to 1606. Translated & edited by Narciso Alonso Cortés. Imprenta del Colegio de Santiago, Valladolid, 1916, pp. 155b-156a, ??NYS.) French translation in: Augustin Redondo; Le jeu de l'énigme dans l'Espagne du XVII^e siècle. Aspect ludique et subversion; IN: Les Jeux à la Renaissance; Actes du XXIII^e Colloque International d'Études Humanistes (Tours, 1980); J. Vrin, Paris, 1982; pp. 445-458, with the problem being on p. 453. There are two brothers, born of the same father and mother. One is my uncle, but the other isn't. How is this possible?

The Book of Merry Riddles. London, 1629. ??NYS -- Santi 235 gives this and says it is reprinted in J. O. Halliwell, The literature of the sixteenth and seventeenth centuries, London, 1851, pp. 67 102, ??NYS, and as pp. 7-29 in Alois Brandl, Shakespeares Book of Merry Riddles und die anderen Räthselbücher seiner Zeit, Jahrbuch der deutschen Shakespeare-Gesellschaft 42 (1906) 1-64, ??NYS. Bryant, pp. 100-102, quotes from: A Booke of Merrie Riddles, Robert Bird, London, 1631 and says it is also known as Prettie Riddles. Santi 237 gives Booke of Merrie Riddles, London, 1631, and says it is reprinted as pp. 53-63 in Brandl, ??NYS. Santi 307 gives The Booke of Merry Riddles, London, 1660, reprinted by J. O. Halliwell in 1866 in an edition of 25 copies, of which 15 were destroyed!, ??NYS. In Bryant, no. 275, pp. 102 & 336: "I know a child borne by my mother, / naturall borne as other children be, / that is neither my sister nor my brother. / Answer me shortly: what is he?"

Boy's Own Book. Conundrums.