Question

There are 20 lines numbered as 1, 2, 3 … 20. All the odd numbered lines intersect at a point and all the even numbered lines are parallel. Find the maximum number of point of intersections.

Answer 1

10 lines are concurrent, 10 lines are parallel.

Odd lines ∈ {I₁, I₃...., I₁₉}

Even lines ∈ {I₂, I₄...., I₂₀}

For maximum intersection:

^{(Even lines)}C₂ × (zero point of intersection) + (One line from odd lines) (one line from even lines) + 1 point of intersection of concurrent lines

⇒ ¹⁰C₂(0) + ¹⁰C₁.¹⁰C₁ + 1

⇒ (101)