<A HREF="https://archive.org/details/TheStanfordMathematicsProblemBook">The Stanford Mathematics Problem Book</A> by George Polya and Jeremy Kilpatrick. > These 20 sets of intriguing problems test originality and insight > rather than routine competence. They involve theorizing and verifying > mathematical facts; examining the results of general statements; > discovering that highly plausible conjectures can be incorrect; > solving sequences of subproblems to reveal theory construction; and > recognizing "red herrings," in which obvious relationships among the > data prove irrelevant to solutions.