Concurs IMAR 2007 - problema 2
Posted: Mon Dec 03, 2007 1:26 pm
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 :
\( \max_{H\in\mathcal{H}} \min_{C\in\mathcal{C}} | H \cap C | \)
\( \min_{H\in\mathcal{H}} \max_{C\in\mathcal{C}} | H \cap C | \)
\( \max_{C\in\mathcal{C}} \min_{H\in\mathcal{H}} | H \cap C | \)
\( \min_{C\in\mathcal{C}} \max_{H\in\mathcal{H}} | H \cap C | \).
\( \max_{H\in\mathcal{H}} \min_{C\in\mathcal{C}} | H \cap C | \)
\( \min_{H\in\mathcal{H}} \max_{C\in\mathcal{C}} | H \cap C | \)
\( \max_{C\in\mathcal{C}} \min_{H\in\mathcal{H}} | H \cap C | \)
\( \min_{C\in\mathcal{C}} \max_{H\in\mathcal{H}} | H \cap C | \).