A. 673. We have colour pearls placed on an \(\displaystyle n\times n\) board; a square may contain more than one pearl. Altogether we used \(\displaystyle 2n-1\) colours and \(\displaystyle n\) pearls from each colour. The pearls are arranged in such a way that no row or column contains more than one pearl of the same colour. Prove that it is possible to select \(\displaystyle n\) pearls with distinct colours such that no two of them are in the same row or column.
Deadline expired on 10 June 2016.