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comb geo with distances among n points in plane

Source: 12th or 13th QEDMO problem 7 (11. - 15. 12. 2013) https://artofproblemsolving.com/community/c2400093_2013_qedmo_13th_or_12th

July 5, 2021
combinatoricscombinatorial geometry

Problem Statement

Let X1,X2,...,XnX_1, X_2,...,X_n be points in the plane. For every ii, let AiA_i be the list of n−1n-1 distances from XiX_i to the remaining points. Find all arrangements of the nn points such all of these lists are the same, except for the order.
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