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Question-149437




Question Number 149437 by SLVR last updated on 05/Aug/21
Commented by SLVR last updated on 05/Aug/21
kindly solution please
$${kindly}\:{solution}\:{please} \\ $$
Answered by Olaf_Thorendsen last updated on 05/Aug/21
• 1−digit numbers :  9 between 1 and 9 ⇒ 9 digits  • 2−digits numbers :  90 between 10 and 99 ⇒ 180 digits  • 3−digits numbers :  900 between 100 and 999 ⇒ 2700 digits    2021 = 9+180+1832  2021 = 9+180+(3×610+2)  The 2021^(th)  digit is the second digit  of 611^(th)  3−digits number.  The 611^(th)  3−digits number is 710.  ⇒ Result is 1.
$$\bullet\:\mathrm{1}−\mathrm{digit}\:\mathrm{numbers}\:: \\ $$$$\mathrm{9}\:\mathrm{between}\:\mathrm{1}\:\mathrm{and}\:\mathrm{9}\:\Rightarrow\:\mathrm{9}\:\mathrm{digits} \\ $$$$\bullet\:\mathrm{2}−\mathrm{digits}\:\mathrm{numbers}\:: \\ $$$$\mathrm{90}\:\mathrm{between}\:\mathrm{10}\:\mathrm{and}\:\mathrm{99}\:\Rightarrow\:\mathrm{180}\:\mathrm{digits} \\ $$$$\bullet\:\mathrm{3}−\mathrm{digits}\:\mathrm{numbers}\:: \\ $$$$\mathrm{900}\:\mathrm{between}\:\mathrm{100}\:\mathrm{and}\:\mathrm{999}\:\Rightarrow\:\mathrm{2700}\:\mathrm{digits} \\ $$$$ \\ $$$$\mathrm{2021}\:=\:\mathrm{9}+\mathrm{180}+\mathrm{1832} \\ $$$$\mathrm{2021}\:=\:\mathrm{9}+\mathrm{180}+\left(\mathrm{3}×\mathrm{610}+\mathrm{2}\right) \\ $$$$\mathrm{The}\:\mathrm{2021}^{\mathrm{th}} \:\mathrm{digit}\:\mathrm{is}\:\mathrm{the}\:\mathrm{second}\:\mathrm{digit} \\ $$$$\mathrm{of}\:\mathrm{611}^{\mathrm{th}} \:\mathrm{3}−\mathrm{digits}\:\mathrm{number}. \\ $$$$\mathrm{The}\:\mathrm{611}^{\mathrm{th}} \:\mathrm{3}−\mathrm{digits}\:\mathrm{number}\:\mathrm{is}\:\mathrm{710}. \\ $$$$\Rightarrow\:\mathrm{Result}\:\mathrm{is}\:\mathrm{1}. \\ $$
Commented by SLVR last updated on 05/Aug/21
yeah...GreatProf. olaf....nice
$${yeah}…{GreatProf}.\:{olaf}….{nice} \\ $$

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