<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.