Dog, sheep, and cabbage
Dog, sheep, and cabbage

A river crossing puzzle is a type of puzzle in which the object is to carry items from one river bank to another, usually in the fewest trips. The difficulty of the puzzle may arise from restrictions on which or how many items can be transported at the same time, or which or how many items may be safely left together.[1] The setting may vary cosmetically, for example, by replacing the river by a bridge.[1] The earliest known river-crossing problems occur in the manuscript Propositiones ad Acuendos Juvenes (English: Problems to sharpen the young), traditionally said to be written by Alcuin. The earliest copies of this manuscript date from the 9th century; it contains three river-crossing problems, including the fox, goose and bag of beans puzzle and the jealous husbands problem.[2]

Solutions to some puzzles charted as timelines

Well-known river-crossing puzzles include:

These problems may be analyzed using graph-theoretic methods,[4][5] by dynamic programming,[6] or by integer programming.[3]

See also


  1. ^ a b Peterson, Ivars (2003), "Tricky crossings", Science News, 164 (24), retrieved 2008-02-07.
  2. ^ p. 74, Pressman, Ian; Singmaster, David (1989), ""The Jealous Husbands" and "The Missionaries and Cannibals"", The Mathematical Gazette, The Mathematical Association, 73 (464): 73–81, doi:10.2307/3619658, JSTOR 3619658.
  3. ^ a b Borndörfer, Ralf; Grötschel, Martin; Löbel, Andreas (1995), Alcuin's Transportation Problems and Integer Programming, Preprint SC-95-27, Konrad-Zuse-Zentrum für Informationstechnik Berlin, archived from the original on 2011-07-19.
  4. ^ Schwartz, Benjamin L. (1961), "An analytic method for the "difficult crossing" puzzles", Mathematics Magazine, 34 (4): 187–193, doi:10.2307/2687980, JSTOR 2687980.
  5. ^ Csorba, Péter; Hurkens, Cor A. J.; Woeginger, Gerhard J. (2008), "The Alcuin number of a graph", Algorithms: ESA 2008, Lecture Notes in Computer Science, vol. 5193, Springer-Verlag, pp. 320–331, doi:10.1007/978-3-540-87744-8_27.
  6. ^ Bellman, Richard (1962), "Dynamic programming and "difficult crossing" puzzles", Mathematics Magazine, Mathematical Association of America, 35 (1): 27–29, doi:10.2307/2689096, JSTOR 2689096.