1. Total no. Of digits used in numbering a book with 366 pages?
2. A printer numbers the pages of a book starting with 1 and uses 3189 digits in all. How many pages does the buk hav?
1. Lets divide the pages from 1-99,100-199,200-299,300-366
all digits occur 20 times from 1-99
so 20(1+2+3+..9)=20*45=
900for 100-199
1 occurs 100 times more hence 900+100=
1000for 200-299
2 occurs 100 times more hence 900+2*100=
1100for 300-366
3 occurs 67 times more hence 900+3*67=
1101so the sum of all the digits is 900+1000+1100+1101=
4101number of digits from 1 to 9 is
9 10 to 99 has 90*2=
180 digits
100 to 366 has 267*3=
801 digitstotal=9+180+801=
990sum of the digits is 4101 and there are 990 digits2.
starting from 1-9 he uses
9 digits
from 10 to 99 he uses 90*2=
180 digits
from 100 to 999 he uses 900*3=
2700 digits
adding these we get 2889 digits
lets subtract this from 3189 , we get
300300/4 will give number of 4 digit pages numbered which is 75;
hence the number of pages is 1000+75-1 (subtract 1 to exclude 1000 which been included in the 75 pages ) ie
1074