What is the minimum number of balls you have to draw to ensure you have at least one ball in every color?

To ensure you have at least one ball of every color, you need to consider the worst-case scenario. If there are ( n ) different colors, you could potentially draw all the balls of ( n-1 ) colors before finally drawing a ball of the last color. Therefore, the minimum number of balls you need to draw to guarantee that you have at least one ball of each color is ( n + (n - 1) = 2n - 1 ).