Let P be a convex polygon with 50 vertices. A set F of diagonals of P is said to be minimally friendly if any diagonal d F intersects at most one other diagonal in F at a point interior to P . Find the largest possible number of elements in

Question

Let P be a convex polygon with 50 vertices. A set F of diagonals of P is said to be minimally friendly if any diagonal d F intersects at most one other diagonal in F at a point interior to P . Find the largest possible number of elements in a minimally friendly set. F .

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Correct answer: 71

Total number of non-intersecting diagonals A₁ A₃, A₁ A₄, A₁ A₅, , A₁ A₄, 47 Total number of intersecting diagonals at only one point to the non-intersecting diagonals A₂ A₄, A₄ A₆, A₆ A₈, , A₄₈ A₅₀ 24 Total =47+24=71

Let P be a convex polygon with 50 vertices. A set F of diagonals of P is said to be minimally friendly if any diagonal d F intersects at most one other diagonal in F at a point interior to P . Find the largest possible number of elements in a minimally friendly set. F .

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