MathDB
Problems
Contests
International Contests
Pan African
2023 Pan-African
4
4
Part of
2023 Pan-African
Problems
(1)
4 numbers with sum more than n/2
Source: PAMO 2023 P4
5/22/2023
Manzi has
n
n
n
stamps and an album with
10
10
10
pages. He distributes the
n
n
n
stamps in the album such that each page has a distinct number of stamps. He finds that, no matter how he does this, there is always a set of
4
4
4
pages such that the total number of stamps in these
4
4
4
pages is at least
n
2
\frac{n}{2}
2
n
. Determine the maximum possible value of
n
n
n
.
combinatorics