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Question Number 149439 by SLVR last updated on 05/Aug/21

Commented by SLVR last updated on 05/Aug/21

$$solutionplease$$

Answered by mr W last updated on 05/Aug/21

$$m\left(n\right)=numberofdigitsofnumbern$$$$m\left(n\right)=1for1⩽n⩽9$$$$m\left(n\right)=2for10⩽n⩽99$$$$m\left(n\right)=3for100⩽n⩽999$$$$m\left(n\right)=4for1000⩽n⩽9999$$$$S\left(k\right)=\underset{n=1}{\sum ^k}m\left(n\right)$$$$S\left(9\right)=9\times 1=9$$$$S\left(99\right)=9\times 1+90\times 2=189$$$$S\left(999\right)=9\times 1+90\times 2+900\times 3=2889>2021$$$$S\left(2021\right)=2889+(2021-999)\times 4=6977$$$$\Rightarrow theresultingnumberhas6977$$$$digits.$$$$\lfloor \frac{2021-189}{3}\rfloor =610$$$$99+610=709$$$$189+610\times 3=2019$$$$the{2021}^{st}digitistheseconddigit$$$$fromthenumber710,i.e.1.$$$$\Rightarrow answerB)$$

Commented by Rasheed.Sindhi last updated on 05/Aug/21

$$\mathbb{W}\mathrm{onderful}\mathrm{mr}\mathbb{W}\mathbf{sir}!$$

Commented by SLVR last updated on 05/Aug/21

$$Thanks..Mr.W..sokindofsir..$$$$extreemlynice..$$$$$$$$$$

Commented by mr W last updated on 05/Aug/21

$$thanksforreviewingsirs!$$

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