Concurs IMAR 2007 - problema 2

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maky
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Concurs IMAR 2007 - problema 2

Post by maky »

Dat fiind un numar intreg \( n>1 \), notam cu \( \mathcal{C} \) familia tuturor configuratiilor de \( n \) puncte situate pe sfera \( S^2 \) si cu \( \mathcal{H} \) familia tuturor emisferelor inchise ale lui \( S^2 \). Determinati :
\( \max_{H\in\mathcal{H}} \min_{C\in\mathcal{C}} | H \cap C | \)

\( \min_{H\in\mathcal{H}} \max_{C\in\mathcal{C}} | H \cap C | \)

\( \max_{C\in\mathcal{C}} \min_{H\in\mathcal{H}} | H \cap C | \)

\( \min_{C\in\mathcal{C}} \max_{H\in\mathcal{H}} | H \cap C | \).
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