Propositiones ad Acuendos Juvenes/Problems/15 - De Homine

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Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $15$

De Homine
A Man Ploughing
How many furrows has a man made,
when he has made $3$ turnings at each end of the field?


Solution

$7$.


Proof

Let the ends of the field be $A$ and $B$.

He starts at $A$ and ploughs the first furrow.
He turns at $B$ and ploughs the second furrow.
He turns at $A$ and ploughs the third furrow.
He turns at $B$ and ploughs the fourth furrow.
He turns at $A$ and ploughs the fifth furrow.
He turns at $B$ and ploughs the sixth furrow.
He turns at $A$ and ploughs the seventh furrow.

$\blacksquare$


Historical Note

Alcuin himself gives $6$ as the answer to this.

Bede correctly gives $7$, as do most translators and interpreters.

It is assumed that Alcuin has made a Fencepost Mistake.

Careful counting, as has been demonstrated here, indicates that the answer is indeed $7$.


Sources

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