# Math Help - Very challenging linear algebra problem (prove there exists an infinite number of spe

1. ## Very challenging linear algebra problem (prove there exists an infinite number of spe

A $n\times n$ matrix which entries from ${1,2,...,(2n-1)}$ is called "special" if for each $i$ the union of the $i$-th row and the $i$-th column contains $(2n-1)$ distinct entries. Prove that there exist no special matrix if $n=2007$. Prove that there exists an infinite number of special matrix.

2. This has nothing to do with linear algebra.
This was a 1997 IMO problem.

3. Good memory.

You can contemplate its solution here.

4. Originally Posted by Krizalid
Good memory.
Thank you. Yes I have good memory.