In a certain convent there were eight large
dormitories on one floor, approached by a spiral staircase in the
centre, as shown in the plan.
On an inspection one Monday by the abbess,
it was found that the south aspect was so much preferred that six times
as many nuns slept on the south side as on each of the other three
She objected to this overcrowding, and ordered that it should be
On Tuesday she found that five times as many slept on the
south side as on each of the other sides.
Again she complained.
Wednesday she found four times as many on the south side, on Thursday
three times as many, and on Friday twice as many. Urging the nuns to
further efforts, she was pleased to find on Saturday that an equal
number slept on each of the four sides
of the house.
What is the smallest number of nuns there could have
been, and how might they have arranged themselves on each of the six
nights? No room may ever be unoccupied.