Question 1193261
.


Formally, there are {{{2^4}}} = 16 different subsets, including empty subset and improper subset.


So, we can expect 16 different sums *), in general case, including the zero sum as one of possible options.


If choosing one or more coins, then the answer is 15 different sums.


-----------


*) if there is no degeneracy . . .