You are erasing the entire numbers, not digits. A few examples looking at the sum $1+2+3$:

• We could erase nothing to get $1+2+3 = 6$
• We could erase everything to get $0$
• We could erase the $2$ to get $1+3 = 4$,
• We could erase $2$ and $3$ to get $1$
• etc.

Basically you're adding up some/none/all of the numbers from the original sum and trying to figure out how many different sums are possible. Hope this helps!