Question

3 STRAIGHT roads can form a maximum of 3 crossings as shown in this figure: What is the maximum number of crossings that can be formed by 4 STRAIGHT roads, given that only two roads meet at a crossing and explain with prompt explanations?

Answer 1

For n straight roads, the maximum number of crossings that can be formed is given by the formula n(n-1)(n-2)/6.

For 4 straight roads, the maximum number of crossings that can be formed is:

4(4-1)(4-2)/6 = 4(3)(2)/6 = 4

To understand why this formula works, we can consider that each pair of roads can potentially intersect at one point. The first road can intersect with (n-1) other roads, the second road can intersect with (n-2) other roads (since it already intersects with the first road), and the third road can intersect with (n-3) other roads (since it already intersects with the first two roads.) However, we must divide the total number of potential intersections by 6, since each intersection is counted three times (once for each road it intersects.)

Therefore, the maximum number of crossings that can be formed by 4 straight roads is 4, as shown in the image below:

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