Propositiones ad Acuendos Juvenes

The medieval Latin manuscript Propositiones ad Acuendos Juvenes (English: Problems to Sharpen the Young) is one of the earliest known collections of recreational mathematics problems.[1] The oldest known copy of the manuscript dates from the late 9th century. The text is attributed to Alcuin of York (died 804.) Some editions of the text contain 53 problems, others 56. It has been translated into English by John Hadley, with annotations by John Hadley and David Singmaster.[2]

The manuscript contains the first known occurrences of several types of problem, including three river-crossing problems:

a so-called "barrel-sharing" problem:

and a variant of the jeep problem:

Some further problems are:

This problem dates back at least as far as 5th century China, and occurs in Indian and Arabic texts of the time.[2], p. 106.
Overtaking problems of this type date back to 150 BC, but this is the first known European example.[2], p. 115.
Alcuin's solution is to note that there are 100 pigeons on the first and 99th steps, 100 more on the second and 98th, and so on for all the pairs of steps, except the 50th and 100th. Note that Carl Friedrich Gauss as a pupil is presumed to have solved the equivalent problem of adding all numbers from 1 up to 100 by pairing 1 and 100, 2 and 99, ..., 50 and 51, thus yielding 50 times 101 = 5050, a solution which is more elegant than Alcuin's solution 1000 years before.[2], p. 121.
This problem seems to be composed for rebuking troublesome students, and no solution is given. (Three odd numbers cannot add up to 300.)[2], p. 121.

References

  1. Alcuin (735-804), David Darling, The Internet Encyclopedia of Science. Accessed on line February 7, 2008.
  2. 1 2 3 4 5 6 7 8 9 10 Problems to Sharpen the Young, John Hadley and David Singmaster, The Mathematical Gazette, 76, #475 (March 1992), pp. 102126.

External links and further reading

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