Bored Reading
Ju read a book. Because he was bored, he decided to total up all of the digits in the page numbers of his book. This time, he counted a total of 17,001 digits. (The first page is labeled "1".)
How many numbered pages did Ju's book contain?
(Please just input the number.)
The answer is 4527.
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1 solution
Pages 1-9 (9 pages) have 1 digit each. (9 pages * 1 digit/page = 9 digits)
Pages 10-99 (90 pages) have 2 digits each. (90 pages * 2 digits/page = 180 digits; running total with previous = 189 digits)
Pages 100-999 (900 pages) have 3 digits each. (900 pages * 3 digits/page = 2700 digits; running total = 2889 digits)
Pages 1000-9999 (9000 pages) have 4 digits each. (9000 pages * 4 digits/page = 36,000 digits) this alone is over the total digits (36,000 > 17001) so the book must run out of pages somewhere in the 4-digit pages. Then, we can compose the following equation:
2889 digits + [ X (pages) * 4 (digits / page) ] = 17,001 digits
Solve for X to find the number of 4-digit pages. BUT! This is not the final answer!
Add X to the previous 999 pages to obtain the final answer, 4527 pages.