Problem #65
Deadline to submit the solution: March 31st
, 2002
Q. How many digits are used to enumerate a 267-page
book?
Hint: For
example, to enumerate a 10-page book,you need 9 digits to enumerate the first 9 pages + 2 digits
forthe 10thpage
(10 has 2 digits: 1 and 0); so altogether you need 11 digits to
enumerate a 10-page book.
Solution:
To enumerate pages:
1 through 10; 11 digits are needed.
11 through 99'; 89 pages x 2 digits = 178 digits
100 through 267; 168 pages x 3 digits = 504 digits
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11 + 178 + 504 = 693 digits are needed to enumerate 267 pages.
