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

• Jun 15th 2008, 09:55 PM
mathwizard
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.
• Jun 16th 2008, 08:14 AM
ThePerfectHacker
This has nothing to do with linear algebra.
This was a 1997 IMO problem.
• Jun 16th 2008, 08:29 AM
Krizalid
Good memory. (Sun)

You can contemplate its solution here.
• Jun 16th 2008, 08:48 AM
ThePerfectHacker
Quote:

Originally Posted by Krizalid
Good memory. (Sun)

Thank you. Yes I have good memory.