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.
This arrangement is crucial to understanding the puzzle of torn pages. If you tear out one sheet, you’re not just removing two consecutive pages, but four pages in total—two from the front and two from the back.
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.
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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.
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