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The Shipman's Puzzle

Of this person we are told, "He knew well all the havens, as they were, from Gothland to the Cape of Finisterre, and every creek in Brittany and Spain.

His barque yclepéd was the Magdalen
The strange puzzle in navigation that he propounded was as follows.

"Here be a chart," quoth the Shipman, "of five islands, with the inhabitants of which I do trade. In each year my good ship doth sail over every one of the ten courses depicted thereon, but never may she pass along the same course twice in any year. 

Is there any among the company who can tell me in how many different ways I may direct the Magdalen's ten yearly voyages, always setting out from the same island?"

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