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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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 […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
