In this article, we’ll dive into the mechanics of book printing and how to determine the number of pages that have been torn out using a bit of logic and math.
In this article, we’ll dive into the mechanics of book printing and how to determine the number of pages that have been torn out using a bit of logic and math. By the end, you’ll be able to solve this common puzzle with ease.
Understanding How Pages in a Book Are Arranged
Books are printed on large sheets of paper that contain multiple pages, not just one. Typically, a single sheet holds four pages: two on the front and two on the back. For instance, in a standard book, the front of the sheet might have pages 1 and 2, while the back would have pages 3 and 4.
Breaking Down the Torn Pages Problem
Let’s consider a specific problem: how many pages are torn out of a book if pages 7 and 8, 100 and 101, and 222 and 223 are missing? This is where the logic of book printing comes into play.
Pages 7 and 8: The First Torn Sheet
When you tear out a sheet that includes pages 7 and 8, you’re also tearing out the back side of that sheet. So, what’s on the back? Pages 5 and 6. Therefore, by removing this one sheet, four pages in total are missing: 5, 6, 7, and 8.
Pages 100 and 101: Another Missing Sheet
Similarly, pages 100 and 101 are printed on one side of a sheet. If you tear out this sheet, the pages on the other side—pages 99 and 102—are also removed. So, this time, four more pages are gone: 99, 100, 101, and 102.
Pages 222 and 223: The Final Torn Sheet
Lastly, let’s consider pages 222 and 223. Just like before, these pages are printed on one side of a sheet, and the back side holds pages 221 and 224. Tearing out this sheet means four more pages are removed: 221, 222, 223, and 224.
