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Explain the proof idea behind the Pigeonhole Principle with one vivid example.
Give me an elegant hint (not the full solution) for a geometry problem with cyclic quadrilaterals.
What’s a surprising connection between prime numbers and randomness?
Create a 3-step plan to practice number theory for Olympiads this week.
Explain Cantor’s diagonal argument for uncountability in simple, rigorous terms.
Suggest 3 paradoxes about infinity with short explanations.
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