Another instance where the " +1 " confusion arises is counting things that are spaced equally.

An example will help. How many drills are there in a standard American drill index - 1/16 to 1/2 by sixty-fourths ?

We can rephrase this problem by noting that 1/16 = 4/64 and 1/2 = 32/64. So, how many drills between 4 and 32 ? One is inclined to say, "Easy. There are 32 between 1 and 32 and four between 1 and 4 so 32 - 4 = 28 drills."

But that's wrong ! If you subtract 4, you're subtracting the 4/64 drill from the sum. You really need to subtract all the drills smaller than 4, which is 3 drills.

Then the correct answer is 32 - 3 = 29

When we generalize this (math alert here) we let 4 be n1 and 32 be n2 and the number of drills between them INCLUSIVE OF BOTH n1 AND n2 is given by:

n2 - (n1 - 1) = n2 - n1 + 1

and there's our " +1 ".

Having this formula in mind, we never need to think through the above again. We simply plug our numbers in and the correct answer falls out.

You'll note that I made use of that formula (without discussion) for "N" in post # 5 above.