I am not a math teacher in the traditional sense.

I just happened to coach math competition preparation since I did it as a kid.

 

For a 10-year-old boy, exhaustive search/case work is definitely highly commendable. But from the point of view of explaining how to solve these types of problems, exhaustive search will not help. As someone pointed out before, if there are N dice instead of 4, a valid method still needs to provide solutions.