One can use calculators to solve some mathematical problems, because in certain cases the problem being solved is not what is being input to the machine.

For example if one has a fence comprised of fence posts and something between the posts (such as wire), then to know the number of gaps, or even the number of posts, one must give a different question to the calculator. To summarise, if we have a fence made up of six posts, then we have five gaps, and thus to divide space (as it were) into five equal portions we must divide by four! :)

Software developers know that situation well, as the dreaded "off by one" error.

FUcking off by one... I do that myself all the time. It has become some sort of OCD... I always have to "prove" that I need to add one, subtract one, or do nothing. It is very annoying.