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KoMaL A Problems
KoMaL A Problems 2017/2018
A. 704
A. 704
Part of
KoMaL A Problems 2017/2018
Problems
(1)
Partitioning triangular board into disjoint unit triangles
Source: KoMaL A. 704
5/21/2023
A regular triangle has side length
n
n{}
n
. We divided its sides into
n
n{}
n
equal parts and drew a line segment parallel with each side through the dividing points. A lattice of
1
+
2
+
…
+
(
n
+
1
)
1+2+\ldots+(n+1)
1
+
2
+
…
+
(
n
+
1
)
intersection points is thus formed. For which positive integers
n
n{}
n
can this lattice be partitioned into triplets of points which are the vertices of a regular triangle of side length
1
1
1
?Proposed by Alexander Gunning, Cambridge, UK
combinatorics