Question 2

We have four sets $$S_1,S_2,S_3,S_4$$ each containing a number of parallel lines. The set $$S_i$$ contains $$i+1$$ parallel lines for $$i=1,2,3,4$$. A line in $$S_i$$ is not parallel to lines in $$S_j$$ when $$i\ne j$$. In how many points do these lines intersect?

Solution

Lines from different sets intersect, while lines within the same set are parallel. Thus the number of intersections is $$2\cdot3+2\cdot4+2\cdot5+3\cdot4+3\cdot5+4\cdot5=71$$. Therefore the correct option is $$71$$.

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We have four sets $$S_1,S_2,S_3,S_4$$ each containing a number of parallel lines. The set $$S_i$$ contains $$i+1$$ parallel lines for $$i=1,2,3,4$$. A line in $$S_i$$ is not parallel to lines in $$S_j$$ when $$i\ne j$$. In how many points do these lines intersect?

Solution

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