The kicker with some of those math competition problems, there will be problems that reduce to finding all natural numbers for which some statement is true. The

The kicker with some of those math competition problems, there will be problems that reduce to finding all natural numbers for which some statement is true. These are almost always small numbers, less than 100 in most circumstances. Which means these problems are trivial to solve if you have a computer - you can simply check all possibilities. And is precisely the reason why calculators aren't allowed. But exhaustive searches are not feasible by hand in the time span the problems are supposed to be solved - roughly 30 minutes per problem. You are not supposed to use brute force, but recognize a key insight which simplifies the problem. And I believe even if you did do an exhaustive search, simply giving the answer is not enough for full points. You would have to give adequate justification.