Problem A. 740. (January 2019)

A. 740. A \(\displaystyle k\times k\) array contains each of the numbers \(\displaystyle 1,2,\ldots,m\) exactly once, with the remaining entries all zero. Suppose that all the row sums and column sums are equal. What is the smallest possible value of \(\displaystyle m\) if \(\displaystyle k=3^n\) (\(\displaystyle n\in\mathbb{N^+}\))?

Proposed by: Attila Sztranyák and Péter Erben,
based on a problem of the 2017 Kalmár competition

(7 pont)

Deadline expired on February 11, 2019.

Statistics:

8 students sent a solution.
7 points:	Csaplár Viktor, Füredi Erik Benjámin, Molnár Bálint, Schrettner Jakab, Szabó Kristóf, Weisz Máté.
5 points:	1 student.
1 point:	1 student.

Problems in Mathematics of KöMaL, January 2019