Try this beautiful problem from the Pre-RMO, 2017 based on Non-Parallel Lines.
Suppose in a plane 10 pairwise non-parallel lines intersect one another. What is the maximum possible number of polygons (with finite areas) that can be formed?
Polygon
Non-parallel lines
Integers
Answer: is 36.
PRMO, 2017, Question 22
Elementary Number Theory by David Burton
Let f(x) be defined as f(x+1)=f(x)+(x+1), f(1)=2 where x is number of lines drawn in a plane which makes the plane into f(x) number of regions
f(2)=f(1)+2=4
f(3)=f(2)+3=7
f(4)=f(3)+4=11
f(5)=f(4)+5=16
f(6)=f(5)+6=22
f(7)=f(6)+7=29
f(8)=f(7)+8=37
f(9)=f(8)+9=46
f(10)=f(9)+10=56
open region for three lines are 6
for 10 lines are 20
so, number of non-overlapping polygon=56-20=36.
Publishing original scientific research in a peer-reviewed journal is an achievement many scholars work toward for years. Achieving this feat early in one's academic journey requires exceptional intellectual rigor, creativity, and persistence. Aaditya Punatar and Muskan Sadana have reached this remarkable milestone, successfully publishing their collaborative research paper in the prestigious Journal of Emerging Investigators […]
Her project on quantum-accelerated Steiner trees for 15-minute cities earned a place among the finalists at the world's largest pre-college STEM competition. Prishaa Shrimali of Marymount School of New York, was selected as a Grand Finalist at the 2026 Regeneron International Science and Engineering Fair (ISEF) in Phoenix, Arizona. Her project was Optimizing Urban Accessibility: […]
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]