a nice little combinatorics problem

We look at the solution to a nice combinatorics problem. In particular, we answer the following:

Is is possible to arrange the numbers 1,2,3,..2020 in an order so that the average of any two numbers in the list is not between these two numbers in the list.

A version of this problem is found in the following book:

102 Combinatorial Problems: https://amzn.to/2YXR4zR

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Books I like:

Abstract Algebra:

Judson(online): http://abstract.ups.edu/
Judson(print): https://amzn.to/2Xg92wD
Dummit and Foote: https://amzn.to/2zYOrok
Gallian: https://amzn.to/2zg4YEo
Artin: https://amzn.to/2LQ8l7C

Differential Forms:
Bachman: https://amzn.to/2z9wljH

Number Theory:

Crisman(online): http://math.gordon.edu/ntic/
Strayer: https://amzn.to/3bXwLah
Andrews: https://amzn.to/2zWlOZ0

Analysis:

Abbot: https://amzn.to/3cwYtuF
How to think about Analysis: https://amzn.to/2AIhwVm

Calculus:

OpenStax(online): https://openstax.org/subjects/math
OpenStax Vol 1: https://amzn.to/2zlreN8
OpenStax Vol 2: https://amzn.to/2TtwoxH
OpenStax Vol 3: https://amzn.to/3bPJ3Bn