With problems like this, I do not begin with a rule (though I can create one after analysis) but with a picture, really a small scale simulation.

What if the numbers were smaller?
- In mind I imagine a small book.

If I start on page 3, and end on page 5, how many pages I have read? I imagine the pages

Part of the difficulty is that we are not quite reading the whole page (and turning each page).
So - if I start at the top of page 3, and turn page 5, I will be looking at the top of page 6. That is where the bookmark will go anywhere.
Now subtraction of page number does work!

Similarly, if I need to end at the bottom of page 4, then I might start turning from the bottom of page 2 (top of page 3) in order to cover two pages.

Alternatively, I might turn page 4 (looking at the top of page 5) so 2 pages starts at the top of page 3.

You are actually trying to count 'whole pages' - but the words suggest an imaginary set up with is not quite complete! Therefore the numbers 'slip' and subtraction/ addition do not quite fit.

You will see I am using visual thinking - but in a way that only some features matter, and I could imagine the picture with pages 99, 100,
54, 55, ... without all the pages in between. This type of reasoning works well in these 'counting problems' - but is often hidden in the books - which quietly assume you will make these 'pictures in your mind' without drawing them (and without them drawing them).

Walter Whiteley
York University