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KoMaL A Problems
KoMaL A Problems 2018/2019
A. 740
A. 740
Part of
KoMaL A Problems 2018/2019
Problems
(1)
Placing 1, ..., m in empty array; row/column sums equal
Source: KöMaL A. 740
2/13/2019
A
k
×
k
k \times k
k
×
k
array contains each of the numbers
1
,
2
,
…
,
m
1, 2, \dots, m
1
,
2
,
…
,
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
m
m
m
if
k
=
3
n
k = 3^n
k
=
3
n
(
n
∈
N
+
n \in \mathbb{N}^+
n
∈
N
+
)?Attila Sztranyák and Péter Erben
combinatorics