## Tuesday, June 21, 2011

### Find The Number of Pages in Printing Book,if Tottal Number of Digits Printed is Given

There is a printed book. The page numbers are not printed. Now the printing of page numbers is being done separately. If the total number of digits printed is 1095 then how many pages does the book have?

There are 9 significant single digit numbers. Hence for the first 9 pages, 9x1 = 9 digits will be printed.

There are 90 significant double digit numbers. Hence for the next 90 pages, 90x2 = 180 digits will be printed. Total number of pages = 99 (90 plus 9), total number of digits is 189(9 plus 180) till now.

Subsequently, we have 900 significant triple digit numbers and 900x3 = 2700 digits. Since the total number of digits printed lies in the range [189, 2889], it suggests that all double digit numbers were printed and some triple digit numbers were printed. The upper limit is arrived at as 2700 plus 189.

Number of digits used to print triple digit numbers = 1095 -189 = 906.

Therefore, 906/3 = 302 triple digit numbers were used.

Therefore the total number of pages printed = 9 plus 90 plus 302 = 401.

That is how solution: 401

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