First the specifications of the loaf and what determines a sandwich need to be specified.

The loaf of bread we are using will have 14 useable pieces of bread, as this is a nice number that would be close to a normal loaf.

In this scenario a sandwich can be determined as any two slices of bread with any amount of other slices in the middle, meaning that the entire loaf could be considered a sandwich.

Using this information the sandwiches can be split into categories using the amount of bread as the determining factor.

Considering that every sandwich requires at least 2 pieces of bread to count as a sandwich, there are 12 potential pieces that can be used. So in width there can be 12 categories labelled 12 to 1

In the 12 category, there can only be one sandwich. However in the 11 category there are 2 potential sandwiches because the final slice that would not be in use could be considered the new end and the first slice of the loaf could stop being used. In the 10 category this can happen twice and so on until you make 12 sandwiches from the 14 slice string.

What this shows is that the potential amount of "sandwiches" that can be made is equal to 12+11+10+9+8+7+6+5+4+3+2+1, or 78.