@xiggi yeah, I’ve seen that problem with the bee and the train. I gotta admit, I think I got tricked and used infinite geometric series the first time I saw that problem.
Another similar SAT-type problem where one should not just try the “obvious” method is something like:
Q: How many 4-digit positive integers greater than 2000 are there whose digits are strictly increasing?
(There are whole books/chapters of books devoted to counting by bijection, which I won’t get into here)
Coming from a math contest background, the most interesting math problems to me have some really creative solution that is harder to find (possibly in addition to an alternate, bashy solution). I feel that the new SAT doesn’t have as many creative problems.