Subj:.....The
Convent Problem (S628)
From the book
"Mathematical Puzzles of Sam Loyd"
Edited by Martin Gardner
From: Dover Publications in 1959
How
many nuns lived in the convent and
what
rooms did they occupy?
The problem of the
Nuns in the Convent of Mt. Maladetta
appears in almost
all collections of puzzles, but it is
childish and the
answer too weak to satisfy the expecta-
tions of solvers.
I remember that the
answer was very disappointing when I
first saw it many
years ago, and I recall the accompany-
ing statement about
the problem being of Spanish origin
and founded on an
incident which occured many centuries
ago. Recently
I came into possession of some very old
Spanish histories,
in one on which I find a brief allusion
to the convent of
Mt. Maladetta, situated on the mountain
of that name, the
highest peak of the Pyrenees. Reference
is made to the occupancy
of that part of the country by
the French invaders
who were finally defeated and driven
out through that
famous pass which was the scene of many
contentions for over
a century.
The direct allusion
to the puzzle, however, occurs in the
passage which says:
"Many of the nuns were carried away by
the 'Frank' soldiers,
which without doubt gave rise to the
familiar problem
of the nuns of the convent of Mt. Maladetta."
As no explanation
of the puzzle is vouchsafed, and the popu-
lar version is so
susceptible of double solutions, I take the
liberty of presenting
it in a form which preserves the spirit
of the problem and
at the same time eliminates the many other
answers.
The convent as shown
in the picture was a square three-story
structure, with six
windows on each side of the upper stories.
It is plain to be
seen that there are eight rooms on each of
the upper floors,
which agrees with the requirements of the
old story.
As the legend goes, the upper floors were used
for sleeping apartments.
The top floor, having more beds in
each of the rooms,
accommodated twice as many occupants as
the second floor.
The Mother Superior,
in accordance with an old rule of the
founders, insisted
that the occupants must be so divided or
arranged that every
room should be occupied; there should be
twice as many on
the top floor as on the second, and there
must always be exactly
eleven nuns in the six rooms on each
of the four sides
of the convent. The problem pertains only
to the two upper
floors, so the ground floor does ont have to
be considered at
all.
Well, it happened
that after the retreat of the French army
through the Pyrenees
pass, nine of the youngest and most
comely nuns were
found to have disappeared. It was always
believed that they
had been captured by the soldiers. Not
to distress the Mother
Superior, however, the nuns who
discovered the loss
found that it was possible to conceal
the fact by judicious
manipulation or change of the occupants
of the rooms.
The nuns managed,
therefore, to readjust themselves in such
a way that when the
Mother Superior made her nightly rounds,
every room was found
to be occupied; eleven nuns on each of
the four sides of
the convent; twice as many on the top
floor as on the second,
and yet the nine nuns were missing.
How many nuns were
there and how were they arranged?
The merit of the
puzzle lies in the paradoxical condition of
the problem, which
strikes us at first to be absolutely
impossible.
Nevertheless it yields so readily to experimental
puzzle methods, when
one knows there is an answer, that our
puzzlists will find
it an amusing and instructive lesson. |
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