Edward is making a book. He writes the page number on each page, starting with page number 1 (1, 2, 3, 4, ...). He will stop as soon as he writes a total of 999 digits. What will be the last page number he writes?
Question
Edward is making a book. He writes the page number on each page, starting with page number 1 (1, 2, 3, 4, ...). He will stop as soon as he writes a total of 999 digits. What will be the last page number he writes?
Solution
To solve this problem, we need to consider how many digits each page number has:
- Pages 1-9: Each of these pages has only 1 digit, so that's 9 digits in total.
- Pages 10-99: Each of these pages has 2 digits, so that's 90 pages * 2 digits = 180 digits.
- Pages 100-999: Each of these pages has 3 digits, so that's 900 pages * 3 digits = 2700 digits.
However, Edward only needs to write 999 digits. He will finish writing all the digits for the pages 1-9 and 10-99, which is 9 + 180 = 189 digits.
This means he still needs to write 999 - 189 = 810 digits. Since each page number from 100 to 999 has 3 digits, he will write 810 / 3 = 270 page numbers from this range.
The last page number he writes will therefore be 99 (the last page number from the 10-99 range) + 270 = 369.
Similar Questions
The total number of digits used to number a 200 page book is:
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