3. The book is sewn from 12 identical booklets. Each booklet consists of several double sheets nested within each other. The booklets of the book are sewn sequentially one after another. All pages of the book are numbered, starting from 1. The sum of the numbers of four pages of one of the double sheets in the fourth booklet is 338. How many pages are in this book?
Solution. Let the book have $x$ pages, then each notebook has $\frac{x}{12}$ pages, the first three notebooks have $\frac{3 x}{12}=\frac{x}{4}$ pages, and the first four notebooks have $\frac{4 x}{12}=\frac{x}{3}$ pages. The numbers of the first and second pages of the fourth notebook will be $\frac{x}{4}+1$ and $\frac{x}{4}+2$, and the numbers of the second-to-last and last pages will be $\frac{x}{3}-1$ and $\frac{x}{3}$. Since the sums of the numbers of all double pages for each of the notebooks are the same, we get the equation $\left(\frac{x}{4}+1\right)+\left(\frac{x}{4}+2\right)+\left(\frac{x}{3}-1\right)+\frac{x}{3}=338$, so $x=288$. Answer: 288.