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Find the set of distinct real numbers

Source: 2019 Jozsef Wildt International Math Competition-W. 5

May 18, 2020
matrix

Problem Statement

Let n≥1n \geq 1. Find a set of distincts real numbers (xj)1≤j≤n\left(x_j\right)_{1\leq j\leq n} such that for any bijections f:{1,2,⋯ ,n}2→{1,2,⋯ ,n}2f : \{1, 2,\cdots ,n\}^2 \to \{1, 2,\cdots ,n\}^2 the matrix (xf(i,j))1≤i,j≤n\left(x_{f(i,j)}\right)_{1\leq i,j\leq n} is invertible.
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