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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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