The three men and their sisters

The medieval Propositiones ad Acuendos Juvenes (“Problems to Sharpen the Young”) is attributed to Alcuin of York (735–804), a leading figure in the “Carolingian Renaissance.” He is the middle person in the image above.

Along with the more famous problem of the wolf, the goat, and the cabbage, Propositiones ad Acuendos Juvenes contains the problem of the three men and their sisters. Three men, each accompanied by a sister, wish to cross a river in a boat that holds only two people. To protect each woman’s honour, no woman can be left with another man unless her brother is also present (and if that seems strange, remember that Alcuin was writing more than 1,200 years ago). In Latin, the problem is:

“Tres fratres erant qui singulas sorores habebant, et fluvium transire debebant (erat enim unicuique illorum concupiscientia in sorore proximi sui), qui venientes ad fluvium non invenerunt nisi parvam naviculam, in qua non potuerunt amplius nisi duo ex illis transire. Dicat, qui potest, qualiter fluvium transierunt, ne una quidem earum ex ipsis maculata sit?”

The diagram below (click to zoom) shows the state graph for this problem. The solution is left (per tradition) as an exercise for the reader (but to see Alcuin’s solution, highlight the white text below the diagram).

Miss A and Mr A cross
Mr A returns (leaving Miss A on the far side)
Miss B and Miss C cross
Miss A returns (leaving Misses B and C on the far side)
Mr B and Mr C cross
Mr B and Miss B return (leaving Miss C and Mr C on the far side)
Mr A and Mr B cross
Miss C returns (leaving 3 men on the far side)
Miss A and Miss C cross
Mr B returns (leaving the A’s and C’s on the far side)
Mr B and Miss B cross

1 thought on “The three men and their sisters

  1. Pingback: Recreational mathematics | Scientific Gems

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