A book has n consecutive pages torn out (each paper in a book has two sides - each side is one page). Suppose A is the last numbered page before the torn out section and B is the first numbered page following the torn-out section. Find a formula for n in terms of A and B.

To find a formula for n in terms of A and B, let's break down the problem. We know that the number of torn-out pages, n, is equal to the number of pages in the torn-out section.

Let's assume A is an even number (if it's odd, we can simply subtract 1 to make it even without changing the result). If A is an even number, then the number of pages before the torn-out section is A/2 (since each side of a paper is counted as one page).

The first numbered page following the torn-out section, B, will be odd. If B is an even number, we can add 1 to make it odd without changing the result.

Now, let's consider the number of pages after the torn-out section. If A is an even number and B is an odd number, we can subtract the number of pages before the torn-out section from the total number of pages after B to find the number of pages in the torn-out section.

The total number of pages in the book is B + 1 (to account for the torn-out section). As each paper has two sides, the total number of pages is (B + 1)/2.

The number of pages after B is (B + 1)/2 - A/2.

Therefore, the formula for n (the number of torn-out pages) in terms of A and B is:
n = [(B + 1)/2 - A/2]

Alternatively, we can simplify the formula further:
n = (B - A + 1)/2