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replacing n, (n + 1) by (n-2) and n, (n + 4) by (n - 1), min negative wanted

Source: RMM Shortlist 2016 C1

July 4, 2019
combinatoricsminimumpositive integers

Problem Statement

We start with any finite list of distinct positive integers. We may replace any pair n,n+1n, n + 1 (not necessarily adjacent in the list) by the single integer n−2n-2, now allowing negatives and repeats in the list. We may also replace any pair n,n+4n, n + 4 by n−1n - 1. We may repeat these operations as many times as we wish. Either determine the most negative integer which can appear in a list, or prove that there is no such minimum.
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