We start with any finite list of distinct positive integers. We may replace any pair n,n+1 (not necessarily adjacent in the list) by the single integer n−2, now allowing negatives and repeats in the list. We may also replace any pair n,n+4 by n−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. combinatoricsminimumpositive integers