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The first sentence tells us that Gus is not the youngest.
The second sentence tells us that neither Alessandro nor Flora is the youngest.
From the third sentence, Oliver is not the youngest, whilst the sixth sentence tells us that Yvette is not the youngest.
So Zara must be the youngest and the order of their ages is Gus, Yvette, Flora, Alessandro, Oliver, Zara.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.