Видеоразбор задачи о рандомных точках на сфере
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A difficult Putnam question with an elegant solution.
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A different write-up of this solution:
1992 Putnam with this problem:
A problem with a similar flavor came up on the 2005 Putnam A6. Give it a try! The solution for that problem, by the way, was written by Calvin Lin, a friend of mine who works at Brilliant. Small world!