Book

To number pages of thick book was used 4201 digits. How many pages has this book?

Result

x =  517

Solution:

c1=9 c2=2⋅ 90=180 c3=3⋅ 900=2700  c4=4201−(c1+c2+c3)=4201−(9+180+2700)=1312  x=9+90+90+c4/4=9+90+90+1312/4=517c_{1}=9 \ \\ c_{2}=2 \cdot \ 90=180 \ \\ c_{3}=3 \cdot \ 900=2700 \ \\ \ \\ c_{4}=4201 - (c_{1}+c_{2}+c_{3})=4201 - (9+180+2700)=1312 \ \\ \ \\ x=9 + 90+ 90+ c_{4}/4=9 + 90+ 90+ 1312/4=517

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