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The hardest problem on the hardest test

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在球面四点形成的四面体问题里,先选穿心直线,再用公平硬币决定端点。这样仍是原来的均匀抽样,却把包住球心的事件变成可以数的符号选择。

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That first line passes through the sphere at two points, so flip a coin to decide which of those two points is going to be p1.

So one and only one of these eight equally likely outcomes gives us a tetrahedron that contains the center.

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