Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Permutation and Combination

Olympiad workbook · IOQM · Permutation and Combination

Let P be a convex polygon with 50 vertices. A set F of diagonals of...

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

Correct answer

71

Step-by-step solution

Total number of non-intersecting diagonals A1A3,A1A4,A1A5,…,A1A4,→47A_1 A_3, A_1 A_4, A_1 A_5, \ldots, A_1 A_4, \rightarrow 47 Total number of intersecting diagonals at only one point to the non-intersecting diagonals A2A4,A4A6,A6A8,…,A48A50→24A_2 A_4, A_4 A_6, A_6 A_8, \ldots, A_{48} A_{50} \rightarrow 24  Total =47+24=71\text { Total }=47+24=71
Practice Permutation and Combination on Quantrex Academy →

More from Permutation and Combination

All Permutation and Combination questions Full Permutation and Combination list All Olympiad workbook PYQs