MathDB
Placing 1, ..., m in empty array; row/column sums equal

Source: KöMaL A. 740

February 13, 2019
combinatorics

Problem Statement

A k×kk \times k array contains each of the numbers 1,2,…,m1, 2, \dots, 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 mm if k=3nk = 3^n (n∈N+n \in \mathbb{N}^+)?
Attila Sztranyák and Péter Erben
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