MathDB
Picking stones from boxes in appropriate ways

Source: Turkey TST 2019 Day 1 P1

March 26, 2019
combinatorics

Problem Statement

In each one of the given 20192019 boxes, there are 20192019 stones numbered as 1,2,...,20191,2,...,2019 with total mass of 11 kilogram. In all situations satisfying these conditions, if one can pick stones from different boxes with different numbers, with total mass of at least 1 kilogram, in kk different ways, what is the maximal of kk?