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Bulgaria Contests
Bulgaria National Olympiad
1979 Bulgaria National Olympiad
Problem 3
Problem 3
Part of
1979 Bulgaria National Olympiad
Problems
(1)
dividing triangle sides, counting triangles without parallel sides
Source: Bulgaria 1979 P3
6/17/2021
Each side of a triangle
A
B
C
ABC
A
BC
has been divided into
n
+
1
n+1
n
+
1
equal parts. Find the number of triangles with the vertices at the division points having no side parallel to or lying at a side of
△
A
B
C
\triangle ABC
△
A
BC
.
combinatorics
geometry
combinatorial geometry
Triangles