Question 34
2014 lines are given in a plane, arranged in three groups of pairwise parallel lines. What is the greatest possible number of triangles formed by the lines (each side from such a triangle lies on one of the lines)?
Macedonian source version, translated in full:
2014 lines are given in a plane, arranged in three groups of pairwise parallel lines. What is the greatest possible number of triangles formed by the lines (each side from such a triangle lies on one of the lines)?
Supplemental illustration (AI-generated):
Schematic showing only a few lines from each group, not all 2014.
Macedonian source version, translated in full:
2014 lines are given in a plane, arranged in three groups of pairwise parallel lines. What is the greatest possible number of triangles formed by the lines (each side from such a triangle lies on one of the lines)?
Supplemental illustration (AI-generated):
Schematic showing only a few lines from each group, not all 2014.