Try this beautiful problem from the Pre-RMO, 2017 based on Average and Integers.
Integers 1,2,3,....,n where n>2, are written on a board. Two numbers m,k such that 1<m<n,1<k<n are removed and the average of the remaining numbers is found to be 17, find the maximum sum of the two removed numbers.
Average
Integers
Maximum
Answer: is 51.
PRMO, 2017, Question 15
Elementary Algebra by Hall and Knight
\(\frac{{n(n+1)}{2}-(2n-1)}{n-2}\)<17<\(\frac{{n(n+1)}{2}-3}{n-2}\)
\(\Rightarrow \frac{n^{2}+n-4n+2}{2(n-2)}<17<\frac{n^{2}+n+6}{2(n-2)}\)
\(\Rightarrow \frac{n-1}{2}<17<\frac{n+3}{2}\)
\(\Rightarrow n<35 and n>31\)
\(\Rightarrow\) n=32,33,34
First case n=32 \(\frac{\frac{n(n+1)}{2}-p}{(n+2)}\)=17
\(\Rightarrow\) p=18
Second case, n=33 \(\Rightarrow\) p=34
Third case, n=34 \(\Rightarrow\) p=51.
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 […]