Using each of the digits $\{1, 2, 3, 4\}$ exactly once and using zero or more $+$ signs, how many different totals can be obtained? no digit can be used as a power, root, etc. only addition can be done. when $n$ digits are written next to each other, they represent an $n$-digit number and not the product of $n$ factors. four of the totals to be included are $\underline{1234}$, $\underline{55} = 12 + 43$, $\underline{127} = 123 + 4$ and $\underline{37} = 31 + 2 + 4$.