KMO 2002 Problem 3

The following facts are known in a mathematical contest:

[list] (a) The number of problems tested was $n\ge 4$ (b) Each problem was solved by exactly four contestants. (c) For each pair of problems, there is exactly one contestant who solved both problems [/list]

Assuming the number of contestants is greater than or equal to $4n$ , find the minimum value of $n$ for which there always exists a contestant who solved all the problems.