1) If I number the pages os a 36 page book, how many digits do I write?
My answers is 63, not sure if this is the correct answer?
2) How many pages does a book have if in numbering them I use:
a) 129 digits? A= 69 pages?
b) 203 digits? A= 104 pages?
Could you please check my answers?
Thank you
1) is what I get too.
2. a) I agree with 69 as well. 63 digits will get you to p36. Another 66 digits will get you another 33 pages.
b) When I calculate this, I get 204 digits for 104 pages:
9 digits for 1-9
180 digits for 10-99
15 digits for 100-104
I think you're probably right, because I don't see how you can make an exact number of pages with 203, but I wonder whether there's a typo.
To find the number of digits required to number the pages of a book, you need to consider the following:
1) If the book has less than 10 pages, you will need to write down as many digits as the number of pages. For example, a 5-page book will require 5 digits.
2) If the book has 10 or more pages, you need to count the number of digits required for each page number.
Now, let's find the number of digits required for each case:
1) A 36-page book:
Since the book has more than 10 pages, we need to calculate the number of digits required for each page number from 1 to 36.
Pages 1-9 require 1 digit each (total: 9 digits).
Pages 10-36 require 2 digits each (total: 54 digits).
Adding up these totals, we get 9 + 54 = 63 digits. Therefore, your answer of 63 digits for a 36-page book is correct.
2) a) A book with 129 digits:
We need to find the number of pages that would require a total of 129 digits.
Pages 1-9 require 1 digit each (total: 9 digits).
Pages 10-99 require 2 digits each (total: 90 digits).
Pages 100 and onwards require 3 digits each (total: 30 digits).
Adding up these totals, we get 9 + 90 + 30 = 129 digits. Therefore, your answer of 69 pages for 129 digits is incorrect.
To find the correct number of pages, we need to consider that:
- We already have 9 digits used for 1-9 pages.
- The remaining 120 digits (129 - 9 = 120) will account for both the 2-digit and 3-digit page numbers.
Since each 2-digit page number requires 2 digits and each 3-digit page number requires 3 digits, we can set up an equation:
2x + 3y = 120
Solving for the positive integer solutions, we find x = 60 and y = 0. This means there are 60 two-digit pages and 0 three-digit pages needed to account for the remaining 120 digits.
Therefore, the correct answer is 9 + 60 = 69 pages.
2) b) A book with 203 digits:
Following the same approach as above:
Pages 1-9 require 1 digit each (total: 9 digits).
Pages 10-99 require 2 digits each (total: 90 digits).
Pages 100 and onwards require 3 digits each (total: 30 digits).
Adding up these totals, we get 9 + 90 + 30 = 129 digits. Therefore, your answer of 104 pages for 203 digits is incorrect.
To find the correct number of pages, we need to consider that:
- We already have 9 digits used for 1-9 pages.
- The remaining 194 digits (203 - 9 = 194) will account for both the 2-digit and 3-digit page numbers.
Again, setting up the equation:
2x + 3y = 194
Solving for the positive integer solutions, we find x = 47 and y = 33. This means there are 47 two-digit pages and 33 three-digit pages needed to account for the remaining 194 digits.
Therefore, the correct answer is 9 + 47 + 33 = 89 pages.
In summary:
a) A book with 129 digits requires 69 pages.
b) A book with 203 digits requires 89 pages.
Please let me know if you need any further clarification!