His visitor was a girl of perhaps twenty-odd. Long straggly hair of indeterminate color strayed over her shoulders. Her eyes, which were large, bore a vacant expression and were of a greenish blue. She wore what were presumably the chosen clothes of her generation--black high leather boots, white open-work woolen stockings of doubtful cleanliness, a skimpy skirt, and a long and sloppy pullover of heavy wool.
Anyone of Poirot's age and generation would have had only one desire--to drop the girl into a bath as soon as possible. He had often felt this same reaction walking along the streets. There were hundreds of girls looking exactly the same. They all looked dirty. And yet--a contradiction in terms--this one had the look of having been recently drowned and pulled out of a river. Such girls, he reflected, were not perhaps really dirty. They merely took enormous care and pains to look so.

Published in 1966, Third Girl drips with disapproval of mod young people. I actually found all the disdain amusing. It's a good thing Christie/Poirot didn't live to see the grunge era.

So this girl, this dirty little hippie girl, shows up at Poirot's home, saying that she thinks she may have committed a murder, but seeing Poirot, she decides he's too old to understand and runs off. Poirot gets help from his old friend Ariadne Oliver, who realizes she's the one who told the girl (Norma) about him during a weekend in the country. Together they eventually track down the girl and get to the bottom of the whole affair, which includes dysfunctional family, an artist boyfriend who's too attractive for his own good, disguises, drugs, and lots more fun. Worth reading if you're a Christie/Poirot completist, but not one of her best.

Solution:

Spoiler

Norma didn't kill anyone. Instead a man posing as her father (who abandoned the family when she was 5) and his partner have been drugging Norma to set her up take the blame for murder. The eventual victim is Norma's pretty artist boyfriend. He painted a portrait of the fake father to replace the actual (dead) father's portrait, then had to be killed because he knew the truth. The real father's former girlfriend also had to be offed because she could recognize the fake father as an imposter. Who committed the murders? The woman posing as both Norma's new step-mother and Norma's roommate (just a wig and a few other changes necessary).