BdMO Regional 2021 Secondary P2
Posted: Tue Mar 30, 2021 4:07 pm
You have six boxes numbered $1, 2, 3, 4, 5$ and $6$ respectively.Your friend has distributed $n$ balls among these boxes. What is the smallest possible value of $n$ for which you can guarantee that there is at least one box that contains at least as many balls as the square of the number written on it?
Or,
There are seven students in a class and their roll numbers are $1, 2, 3, 4, 5, 6$ and $7$ respectively. They have distributed $k$ taka among themselves where $k$ is a positive integer. What is the smallest possible value of $k$ for which you can guarantee that there exists a student with at least as much taka as the square of their roll number?
Or,
There are seven students in a class and their roll numbers are $1, 2, 3, 4, 5, 6$ and $7$ respectively. They have distributed $k$ taka among themselves where $k$ is a positive integer. What is the smallest possible value of $k$ for which you can guarantee that there exists a student with at least as much taka as the square of their roll number?