Question

There are 20 lines numbered as 1,2,3,..., 20. And 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

Correct Answer: 101

To determine the maximum number of intersection points from the given configuration of lines, consider these steps:

1. Define the line characteristics: Odd-numbered lines (1, 3, 5,...,19) intersect at a common point. Even-numbered lines (2, 4, 6,...,20) are parallel.

2. Calculate intersections among lines:

- Odd-numbered lines: There are 10 such lines. They intersect at a single point, contributing 1 unique intersection.

- Odd with Even lines: Since there are 10 odd-numbered lines that intersect any given even-numbered line at a unique point, and there are 10 even-numbered lines, the intersections are given by: 10 (odd) × 10 (even) = 100 intersection points.

3. Total intersections: Sum of intersections = 1 (odd-odd) + 100 (odd-even) = 101.

4. Confirmation with given range: The calculated sum is 101, which fits within the provided range (101,101).

Hence, the maximum number of intersection points is 101.