This type of problem might be good to reward the reader / student for clever and not brute force attacks. This problem is simple enough to brute force through it but add in a few extra digits and more rules would stop that. So I can use one like this as an example then grow the string to make the problems harder. I also think this problem would be better with crossed patterns – sort of like numeric scrabble. I think I have seen math puzzle books in the airports with patterns like this. Probably something like what they are doing.
Any way – the problems it:
