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 sides. 
She objected to this overcrowding, and ordered that it should be reduced. 
On Tuesday she found that five times as many slept on the south side as on each of the other sides. 
Again she complained. 
On 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.

See answer

Math Genius