Combinations of digits that sum up to 2 are either 1+1 or 2+0:Combinations 1+1:Double Digits
11 Total: 1Triple Digits
110 Total: 2 Quadruple Digits
1100 Total: 3
So now the pattern emerges that for every N digit number, there are N-1 combinations summing up to two. The number of integers should be between 1 and 10^21, exclusive which means that the largest allowed integer does only have 21 digits, not 22 which means that the amount combinations with the largest amount of places is 20 (21-1).
We can thus calculate the total amount of integers that satisfy the question by calculating the set of consecutive integers: 1+2+3...+20 which is 210. However, we did not account for the combinations of 2 and 0 that sum up to two, we have to add them first:Combinations 2+0:Single Digit
2 Total: 1Double Digits
20 Total: 1Triple Digits
200 Total: 1
This pattern is obviously easier to comprehend and will account for an additional 21 combinations.
Hence: 210+21 = 232.
Sorry for my rusty English, I am not a native speaker