How many pages have been torn from the book?

At first glance, figuring out how many pages have been torn from a book might seem simple. However, understanding how books are printed and how pages are arranged can help shed light on this common puzzle. In most cases, a single sheet of paper contains two printed pages on each side, making it essential to consider how sheets and pages relate to one another.

In this article, we’ll break down how to solve the question, “How many pages have been torn from the book?” using logic and a bit of math, focusing on the relationship between pages and sheets of paper in a typical book.

Understanding How Book Pages Are Arranged

Books are traditionally printed in such a way that a single sheet of paper contains four pages. That means two pages are printed on the front of the sheet, and two pages are printed on the back. For example, in a standard book, pages 1 and 2 would be printed on the front of the sheet, while pages 3 and 4 would be on the back.

This is a crucial concept because when you tear out one sheet, you’re not just removing two consecutive pages—you’re removing four pages in total, two from the front and two from the back of the sheet.

Identifying the Torn Pages

Let’s go over the problem of determining how many pages were torn out from a book when specific pages like 7 and 8, 100 and 101, and 222 and 223 are missing.

1. Pages 7 and 8 are printed on the same side of the sheet. Since pages are printed in pairs, this also means that pages 5 and 6 are on the back side of the same sheet. Thus, by tearing out the sheet containing pages 7 and 8, you are also removing pages 5 and 6 from the back.So, tearing out this sheet results in four pages being removed: pages 5, 6, 7, and 8.
2. Pages 100 and 101 are likewise part of the same sheet of paper. The page sequence continues in this manner, meaning pages 99 and 102 are printed on the opposite sides of the same sheet. By removing this sheet, you are again tearing out four pages: pages 99, 100, 101, and 102.
3. Pages 222 and 223 follow the same rule. Tearing out this sheet also removes the corresponding back pages, which would be 221 and 224. Thus, tearing out this sheet results in the removal of four pages: pages 221, 222, 223, and 224.

Total Pages Torn Out

To find out how many total pages have been torn from the book, we simply add up all the missing pages.

• From the first sheet (pages 5-8), 4 pages are torn out.
• From the second sheet (pages 99-102), another 4 pages are torn out.
• From the third sheet (pages 221-224), an additional 4 pages are removed.

In total, this means that 12 pages have been torn out of the book.

Conclusion: How Many Pages Were Removed?

To summarize, when considering the way books are printed and arranged, we can conclude that 12 pages were torn from the book based on the specified missing pages. It’s important to understand that tearing out a single sheet removes four pages, as each sheet contains two pages on the front and two on the back.

By following this logic and understanding the mechanics of book printing, you can solve similar problems with ease. This approach is helpful in determining missing pages and understanding the structure of printed materials.