At first glance, determining how many pages were torn from a book might seem like a straightforward task. However, when you consider how books are printed and bound, the situation becomes a little more complex. Pages in a book are printed on both sides of a sheet of paper, which means when you tear out a single sheet, you’re actually removing two pages at once. In this article, we’ll break down the process of understanding how many pages have been torn from a book and dive into the logic behind it.
Before diving into the numbers, it’s essential to understand how pages are organized within a book. Books are typically printed on large sheets of paper, which are then folded and cut to create individual pages. Each sheet in a book contains two pages on each side—one odd-numbered page and one even-numbered page. For example, if you open a book, you’ll see that page 1 is printed on the front, while page 2 is on the back of the same sheet.
This concept is crucial when trying to figure out how many pages are torn from a book because removing one sheet means removing two pages—the front and the back.
Let’s consider a hypothetical situation where pages are torn from a book. For example:
- Pages 7 and 8 are torn out.
- Pages 100 and 101 are torn out.
- Pages 222 and 223 are torn out.
The goal is to determine how many pages have been removed in total.
Step 1: Recognizing Each Torn Sheet
The key to solving this problem is realizing that a page number alone does not correspond to just one page; it represents one side of a sheet of paper. As such, each set of torn pages represents a single sheet being removed.
- Pages 7 and 8 are printed on the same sheet of paper. When you tear out this sheet, you remove both pages.
- Similarly, pages 100 and 101 are on the same sheet. Tearing out this sheet means both of these pages are gone.
- Lastly, pages 222 and 223 are also on the same sheet, so tearing out this sheet removes both of these pages.
Step 2: Counting the Sheets Removed
Each of the three pairs of pages (7 and 8, 100 and 101, 222 and 223) represents one sheet being torn out of the book. Therefore, we can calculate that:
- 1 sheet was removed when pages 7 and 8 were torn out.
- 1 sheet was removed when pages 100 and 101 were torn out.
- 1 sheet was removed when pages 222 and 223 were torn out.
In total, 3 sheets of paper were torn out.
Step 3: Calculating the Total Number of Pages Removed
Since each sheet contains two pages—one on the front and one on the back—the total number of pages removed can be calculated by multiplying the number of sheets by two:
- 3 sheets × 2 pages per sheet = 6 pages in total.
Therefore, 6 pages were removed from the book.
The mistake many people make when trying to determine how many pages were torn out is forgetting that books are printed on both sides of a sheet. When you tear out a page like “page 7,” you are also removing “page 8” because they are part of the same sheet. This logic applies to every pair of torn pages.
Understanding how pages are printed on both sides of a sheet is crucial when trying to determine how many pages have been removed from a book. Whether you’re a book lover, a printer, or simply someone solving a puzzle, keeping this logic in mind will help you arrive at the correct answer every time.
