MathDB

A museum has the shape of a

n \times n

square divided into

n^2

rooms of the shape of a unit square

(n>1)

. Between every two adjacent rooms (i.e. sharing a wall) there is a door. A night guardian wants to organize an inspection journey through the museum according to the following rules. He starts from some room and, whenever he enters a room, he stays there for exactly one minute and then proceeds to another room. He is allowed to enter a room more than once, but at the end of his journey he must have spent exactly

k

minutes in every room. Find all

n

and

k

for which it is possible to organize such a journey.

Problem Statement