MathDB
Problems
Contests
National and Regional Contests
Mexico Contests
Mexican Quarantine Mathematical Olympiad
#2
#2
Part of
Mexican Quarantine Mathematical Olympiad
Problems
(1)
Classrooms with rare capacities
Source: Mexican Quarantine Mathematical Olympiad P2
4/25/2020
Let
n
n
n
be an integer greater than
1
1
1
. A certain school has
1
+
2
+
⋯
+
n
1+2+\dots+n
1
+
2
+
⋯
+
n
students and
n
n
n
classrooms, with capacities for
1
,
2
,
…
,
n
1, 2, \dots, n
1
,
2
,
…
,
n
people, respectively. The kids play a game in
k
k
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
n
n
, determine the greatest possible value of
k
k
k
.Proposed by Victor Domínguez
combinatorics
relations