The same decomposition works in higher dimensions. For NNN random points on a sphere, the probability they all lie in a hemisphere is also N/2N−1N / 2^{N-1}N/2N−1. The argument is identical: anchor a hemisphere at each point, observe that each event has probability 1/2N−11/2^{N-1}1/2N−1, and verify that at most one anchor can work (the complementary cap is at least a full hemisphere, so no other anchor's hemisphere can straddle it). TODO: If I figure out how to add 3d visualizations to this website, I'll cover the 3D case
Раскрыты подробности похищения ребенка в Смоленске09:27
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How does a splitting factor work?
An Advanced Camera System to Capture Everyday Moments
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Силовые структуры。关于这个话题，服务器推荐提供了深入分析
# Score all pairs (~65s, 235,625 comparisons)