Challenge and Thrill of Pre-College Mathematics by V.Krishnamuthy , C.R.Pranesachar, ect. [/et_pb_accordion_item][/et_pb_accordion][et_pb_text _builder_version="3.27.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" custom_margin="48px||48px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3" inline_fonts="Aclonica"]
Do you really need a hint? Try it first!
[/et_pb_tab][et_pb_tab title="Hint 1" _builder_version="3.22.4"]Let \(n\) be a \(k\) digit(s) number number , then \(n\) can be written as \(n=a_0+10a_1+10^2a_2+\cdots+10^{k-1}a_{k-1}\)Where ,\(a_0,a_1,...,a_{k-1}\) are digits of \(n\).
[/et_pb_tab][et_pb_tab title="Hint 2" _builder_version="3.22.4"]\(a_0,a_1,...,a_{k-1} \in [1,9] \) as the range of the function \(g\) is \(\mathbb{N}\)\(\Rightarrow a_0,a_1,...,a_{k-1}\neq 0\) .Now \(g(n)=a_0a_1a_2\cdots a_{k-1}\le \underbrace{10\cdot10\cdot10\cdots 10}_{(k-1) times} \cdot a_{k-1}\) [Since \(a_0,a_1,...,a_{k-1} \le 10 \)] Equality holds when \(k=1\) .
[/et_pb_tab][et_pb_tab title="Hint 3" _builder_version="3.22.4"]\(\Rightarrow g(n)\le 10^{k-1}\cdot a_{k-1}\)\(\Rightarrow g(n)\le 10^{k-1}\cdot a_{k-1}+\cdots+10^2a_2+10a_1+a_0\) [Since \(a_0,a_1,...,a_{k-1} >0\)] \(\Rightarrow g(n)\le n\) (Proved) .
[/et_pb_tab][et_pb_tab title="Hint 4" _builder_version="3.22.4"]\(n^2-12n+36=g(n)\)\(\Rightarrow n^2-12n+36 \le n\) [Since \(g(n) \le n\) ]\(\Rightarrow n^2-13n+36 \le 0\)\(\Rightarrow (n-9)(n-4) \le 0\)\(\Rightarrow 4\le n\le 9\)\(\Rightarrow n={4,5,6,7,8,9}\) (Ans.) .
[/et_pb_tab][/et_pb_tabs][et_pb_text _builder_version="3.27.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" min_height="12px" custom_margin="50px||50px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3" inline_fonts="Aclonica"]Indian Statistical Institute and Chennai Mathematical Institute offer challenging bachelor’s program for gifted students. These courses are B.Stat and B.Math program in I.S.I., B.Sc. Math in C.M.I.
The entrances to these programs are far more challenging than usual engineering entrances. Cheenta offers an intense, problem-driven program for these two entrances.
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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 […]
