I second the idea that learning real math will help, but there is a purpose to using "logic puzzles" also - math doesn't help much with learning to recognize various "difficulties" - cognitive biases, like framing issues, and common fallacies, like ad hominems. Besides practicing logic puzzles, you need a good overview book, Robyn Dawes, Rational Choice in an Uncertain World, is the single best volume I have found.
Are we talking about the same kinds of "logic puzzles"?