Brilliant's Mathematical Contest!
Logic
Level
5
In a Mathematics Contest conducted by Brilliant, only the following facts are known to its staff:
The number of problems asked in the contest was \({n \geq 4}\).
Each problem was solved by exactly four contestants.
For each pair of problems, there is exactly one contestant who solved both the problems.
Assuming that the number of contestants is greater than or equal to \({4n}\), help the staff find the minimum value of \({n}\) for which there always exists a contestant who solved all the problems.
Image Credit: MissiouriState.edu.
by
Satyajit Mohanty