You might want to look into the maths related to various paradoxes: unexpected hanging, Raven paradox, liar paradox, two envelopes problem, Zeno's paradox, Blue Eyes problem and game theory like the Prisoner's dilemma. Wikipedia, Math Stackexchange and Less Wrong have much discussion on these paradoxes.

If you want to improve your rationality, it's not enough to just know the solution. You have think very carefully about what reasoning made you believe the incorrect answer in the first place and how to adjust your intuitions so that they are correct.