A museum has the shape of a n×n square divided into n2 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. combinatorics proposedcombinatorics