I thought of the following problem:
Let $n\ge 2$. Suppose you have $n^2$ distinct numbers in some field. Is it necessarily possible to arrange the numbers into an $n\times n$ matrix of full rank (ie, nonsingular or invertible)?
(I am able to solve the problem, for example using the combinatorial nullstellensatz.)
I was wondering whether this problem was previous stated elsewhere, perhaps even on this site?
My original motivation for the problem was in fact quite similar to this question, but I was rearranging the primes.