Good girls and bad boys (1)
On an island, there is this strange pattern - boys always lie while girls always tell the truth. You encounter two children.
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The older one says: "We are of the same gender."
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The younger one says: "We are of opposite genders."
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The two statements contradict each other. Obviously, one must be true, the other must be false. Since we know boys lie while girls tell the truth, one must be a girl, the other a boy. We now can tell that the two are of opposite genders so the older one is a liar (and hence a boy) while the younger one is a truth teller (and hence a girl).