MathDB

Let

n

be an integer greater than

1

. A certain school has

1+2+\dots+n

students and

n

classrooms, with capacities for

1, 2, \dots, n

people, respectively. The kids play a game in

k

rounds as follows: in each round, when the bell rings, the students distribute themselves among the classrooms in such a way that they don't exceed the room capacities, and if two students shared a classroom in a previous round, they cannot do it anymore in the current round. For each

n

, determine the greatest possible value of

k

.
Proposed by Victor Domínguez

Problem Statement