A box contains 5 sets of balls while there are 3 bails in each set. Each set of balls has one colour which is different from every other set. What is the least number of balls that must be removed from the box in order to claim with certainty that a pair of bails of the same colour has been removed?

To solve this, we use the Pigeonhole Principle. The box contains 5 different colors, with 3 balls of each color. To ensure with certainty that you have a pair of the same color, you must consider the worst case scenario. The worst case scenario is that every ball you pick is a different color. Since there are 5 different colors, you could potentially pick 5 balls where each one is a different color. At this point, you have one ball of each color but no pair. When you remove the 6th ball, it must be one of the 5 colors already picked. Therefore, the 6th ball will inevitably form a pair with one of the balls already removed. Thus, the least number of balls required to guarantee a pair of the same color is 6. Correct Answer: A