<p>Hard math problems require some careful thinking but are never that bashy and no problem should take more than 1-2 minutes. But 50% of the hard problem is usually just breaking down the hard problem into smaller pieces, and careful reading.</p>
<p>For example, a lot of students seem to mix up “could be true” and “must be true.” If P is true for some cases, you can’t really determine whether P must be true. To determine whether P must be true, either prove that it is true, or find one counterexample. To show whether P could be true, either prove that it can’t be true, or find one case where it is true.</p>