In the village church, said the priest to the parish clerk: - It is funny to see that those three ladies...

logic/priest.and.ladies New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

In the village church, said the priest to the parish clerk:
- It is funny to see that those three ladies down there in the benches
who always attend my sermons are not only linked together by their
strong religiousness but also arithmetically.
- How so, father? replied the parish clerk.
- Well, you see, you could decide their individual ages by the simple
facts that their ages summed are 168 and their ages multiplied are
171600.  Is not that a lovely whim of God's hand? said the priest with
his eyes wandering off to the ceiling, or beyond.

The parish clerk, with his slight talent for mental arithmetic, thought
for a moment and then said to the priest:
- Forgive me father, but I believe you are wrong in your saying.
- Oh, but you forget that I am the oldest, my son, said the priest with
a smile.
- Yes, of course, there you have it, said the parish clerk with a sigh.

How old were the three ladies, and how old was the priest?

-- Niklas Agren <niklas@heat.kth.se>

Show solution

There are only two sets of numbers which meet the numerical
constraints.  They are:

        [48, 55, 65]
        [50, 52, 66]

We must use the fact that the priest is older than the three women to
disqualify one of these solutions.  If the priest were to be 65 or
younger, there would be no solution.  If the priest were 67 or older,
both solutions would be valid.  Thus, the priest is 66, and the women
are 48, 55, and 65.

-- ga82428@inet.d48.lilly.com  (June 1994)