How would we know to use 100?
Try an example.
I did the following:
A = 2 B = 3 C = 5
ABC = 235
BCA = 352
CAB = 523
Therefore, 235 + 352 + 523 = 1110
1110’s largest divisible integer is 111
I know that’s the right answer, but is my logic behind it correct?
Other than the rigour (which is fine since you simply used an example), yes.