Boxes without principle
Source: 1st German pre-TST 2006, problem 2
December 5, 2005
inequalitiescombinatorics proposedcombinatorics
Problem Statement
In a room, there are boxes, each of them containing one or several sorts of fruits, and of course an integer amount of each fruit.
a) Show that we can find boxes, which altogether contain at least a third of all apples and at least a third of all bananas.
b) Can we always find boxes, which altogether contain at least a third of all apples, at least a third of all bananas and at least a third of all pears?