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Distance from it to O does not exceed 574

Source: IMO LongList 1988, Poland 2, Problem 59 of ILL

November 3, 2005
geometry3D geometryspheregeometry unsolved

Problem Statement

In 33-dimensional space there is given a point OO and a finite set AA of segments with the sum of lengths equal to 19881988. Prove that there exists a plane disjoint from AA such that the distance from it to OO does not exceed 574574.
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