bmehmet David do you think 12sums could possibly work when you break it down into pairs as well? For pairs you have sums 0-18
Example number 352, broken down into pairs
pair 35 sum of 08 (12sum 1,2)
Pair 32 sum of 05 (12sum 1,1)
Pair 52 sum of 07 (12sum 1,1)