Kvant Math Problem 1265

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Verified: no
Verdicts: SKIP + SKIP
Solve time: 7m40s
Source on kvant.digital

Problem

  1. Prove that among the 21 pairwise distances between 7 distinct points in the plane, the same number can appear at most 12 times.
  2. What is the maximum number of times the same number can appear among the 15 pairwise distances between 6 distinct points in the plane?

N. M. Sedrakyan

Working