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Combinatorial 3D geometry

Source: Czech and Slovak Olympiad 1981, National Round, Problem 6

October 11, 2024
geometrycombinatorial geometry3D geometry

Problem Statement

There are given 11 distinct points inside a ball with volume V.V. Show that there are two planes ϱ,σ,\varrho,\sigma, both containing the center of the ball, such that the resulting spherical wedge has volume V/8V/8 and its interior contains none of the given points.
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