Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 673. (May 2016)

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.

(5 pont)

Deadline expired on June 10, 2016.

### Statistics:

 3 students sent a solution. 5 points: Williams Kada. 3 points: 1 student. 2 points: 1 student.

Problems in Mathematics of KöMaL, May 2016