Alice is visiting the Maths section of her local library. She takes a large old book from the shelf and sits down at a desk to read. The book falls open somewhere in the middle. Alice is initially disappointed to see that the left hand and right hand page numbers are not consecutive – there are a number of pages missing. But Alice is delighted to note that, read left to right, the digits of the two page numbers form a consecutive descending sequence of digits. What is the minimum number of pages that could be missing from the book?
The page numbers in the original book start at one and each page is numbered sequentially.
[I really like this puzzle, thank you! Harry]