I request a hint, clarification (if needed), or your approval (if my doutful solution is correct) for this problem:
Problem 3. Jack tore out several successive pages from a book. The number of the first page he tore out was 183, and it is known that the number of the last page is written with the same digits in some order. How many pages did Jack tear out of the book?
Every hint or clarification you propose is really acknowledged. Here's the link of the book in case you need it.
Here's my doubtful solution:
There are five possibilities of values of the last page: $138$ is forbidden; otherwise, $813$, $831$, $318$, $381$ are valid. Since the verso of the last page must be even, we consider $318$ the number of the last page. Hence Jack tore out 67 pages.
Thank you very much!
P.S. You may note that the book has a section of answers and hints. However, I had the misfortune of carrying the unpleasant feeling of accidentally seeing the solution of an interesting problem. This, of course, ruined the amusement at searching for that solution. This site is not an exception. Moreover, I noticed this same question here; but, the difference between my question and that question posted there is that he gave the answer. Hence I eagerly wish to discuss the problem, and solve it (being given your approval) without seeing the answer. Without seeing the answer and receiveing feedback, I own the possibility of re-thinking my answer, refining it, and improving my mathematical thinking. This is by far the most important exercise for me.
P.S.S. I am not an English-native speaker, so every correction to my writing is really appreciated!