Propositiones ad Acuendos Juvenes/Problems/13 - De Rege et de Eius Exercitu/Historical Note

Historical Note on Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $13$: De Rege et de Eius Exercitu

This is seen to be an example of the Wheat and Chessboard Problem, taken to not quite as great an extreme.

John Hadley and David Singmaster, in their translation of Propositiones ad Acuendos Juvenes, give Alcuin's complete solution, which consists of documenting each of the powers of $2$ in turn:

After the first stop there were $2$ men; after the second $4$; after the third $8$; after the fourth $16$; ... after the twenty-ninth $536870912$; after the thirtieth $1073741824$.

Singmaster goes on to note that in some of the historical manuscripts that propagate this problem, a number of them have incorrect values.

Sources

• 1992: John Hadley/2 and David Singmaster: Problems to Sharpen the Young (Math. Gazette Vol. 76, no. 475: pp. 102 – 126)  www.jstor.org/stable/3620384