self Maths Puzzle

Five intersecting straight lines are drawn in a plane. What is the minimum and maximum number of points of intersection? What is the maximum number of triangles that can be formed?

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self Other Question

In a certain there are four states. Each state has four major cities. All the major cities in a state are connected with each other via three different modes of transport namely rail, road and air. But a city is connected a another city via only one mode of transport if it belongs to the other states. What is the total number of different routes constructed among the major cities in the given country? Find the number of integral solutions of the equation x + y + z = 20 where x, y, z > 0.