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Finding the erased distance with the other distances...

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February 19, 2011
geometry unsolvedgeometry

Problem Statement

There are 100100 points on the plane. All 49504950 pairwise distances between two points have been recorded. (a)(a) A single record has been erased. Is it always possible to restore it using the remaining records? (b)(b) Suppose no three points are on a line, and kk records were erased. What is the maximum value of kk such that restoration of all the erased records is always possible?