Propositiones ad Acuendos Juvenes/Problems/1 - De Limace

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $1$

De Limace

A Slug

A leech invited a slug for lunch a leuca away.

But he could only walk an inch a day.

How many days will he have to walk for his meal?

Solution

$90 \, 000$ days, or $246$ years and $210$ days.

(This does not take into account leap years, as it assumes a year of strictly $365$ days.)

Proof

It is understood that there are:

$1500$ paces to a leuca

$60$ inches to a pace.

Hence there are $90 \, 000$ inches to a leuca.

Thus at $1$ inch per day, it will take the slug $90 \, 000$ days to arrive for his meal.

$\blacksquare$

Sources

• c. 800: Alcuin of York: Propositiones ad Acuendos Juvenes ... (next)
• 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