Let we are having 3 points, A1, A2, A3. The broken line would be (A1)(A2)(A3). Since there are 2 lines with common vertex A2, so intersection phenomenon is impossible. But if we have 4 points & create a crossed(*) quadrilateral, there would be an intersection between 2 opposite sides of the quadrilateral. So maximum value of n is 3

(*)in জ্যামিতির ২য় পাঠ, there's mentioned that quadrilateral are of 3 types and one of them is crossed, where 2 opposite sides intersects.

(*)in জ্যামিতির ২য় পাঠ, there's mentioned that quadrilateral are of 3 types and one of them is crossed, where 2 opposite sides intersects.