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

Commented bySLVR last updated on 05/Aug/21

solution please

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

m(n)=number of digits of number n m(n)=1 for 1≤n≤9 m(n)=2 for 10≤n≤99 m(n)=3 for 100≤n≤999 m(n)=4 for 1000≤n≤9999 S(k)=Σ_(n=1) ^k m(n) S(9)=9×1=9 S(99)=9×1+90×2=189 S(999)=9×1+90×2+900×3=2889>2021 S(2021)=2889+(2021−999)×4=6977 ⇒the resulting number has 6977 digits. ⌊((2021−189)/3)⌋=610 99+610=709 189+610×3=2019 the 2021^(st) digit is the second digit from the number 710, i.e. 1. ⇒answer B)

Commented byRasheed.Sindhi last updated on 05/Aug/21

Wonderful mr W sir!

Commented bySLVR last updated on 05/Aug/21

Thanks..Mr.W..so kind of sir.. extreemly nice ..

Commented bymr W last updated on 05/Aug/21

thanks for reviewing sirs!