Complicated operation
Source: Kvant Magazine No. 11 2019 M2584
March 20, 2023
combinatoricsOperation
Problem Statement
We have 2019 boxes. Initially, they are all empty. At one operation, we can add exactly 100 stones to some 100 boxes and exactly one stone in each of several other (perhaps none) boxes. What is the smallest possible number of moves after which all boxes will have the same (positive) number of stones.Proposed by P. Kozhevnikov