Triple trouble
Irene is one of a set of identical triplets. One of her sisters always tells the truth, and the other one always lies. Irene sometimes is truthful and sometimes isn't.
The triplets are dressed in identical outfits except for the ribbons in their hair. One girl has a blue ribbon, one a green ribbon, and one a red ribbon.
"Irene?" you call out, questioningly.
"That's me," says the girl wearing a blue ribbon.
"Yep, she's Irene," agrees the girl wearing a green ribbon.
"I'm definitely not Irene," says the girl wearing a red ribbon.
Which triplet is Irene?
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If the girl wearing a blue ribbon were Irene, they'd all be telling the truth, which is impossible since one of her sisters always lies.
If the girl wearing a red ribbon were Irene, they'd all be lying, which is impossible since one of her sisters is always truthful.
So Irene must be the girl wearing a green ribbon (and is lying). Her sister wearing red ribbon is the truth-teller, her sister wearing the blue ribbon is lying.