Question 5
There are 2019 cards bearing distinct positive integers at most 2019. Does there exist a positive integer $n$ such that all cards can be placed in $n$ boxes, with the cards in each box divisible into two groups so that one group’s label sum equals $\frac27$ of the other group’s label sum?
For a group containing one card, its sum is that card’s label.
For a group containing one card, its sum is that card’s label.