MathDB

220 triangles with k +s points on 2 parallel lines

Source: Argentina 1997 OMA L3 p1

May 13, 2024

combinatoricscombinatorial geometrygeometry

Problem Statement

Let

s

and

t

be two parallel lines. We have marked

k

points on line

s

and

n

points on line

t

(

k\geq n

). If it is known that the total number of triangles that have their three vertices at marked points is

220

, find all possible values of

k

and

n