A bag contains several balls of the same size and of five different colors. The number of balls of each kind is $$16$$, $$26$$, $$34$$, $$24$$ and $$40$$. Now pick the balls without observing them. How many balls have to be picked at least in order to ensure you get $$16$$ balls of one color together with $$13$$ balls of another color? 
Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems