You have b bins, each with 3 random marbles. There are n different colors of marbles and 2 different designs (solid and striped). Your goal is to choose one marble from each bin; however, you may only choose one design for each color of marble (duplicates of the same color+design are allowed). What is the fastest method to determine if it is even possible to choose a marble from each bin while following these constraints? Judge the speed of your method in terms of n and assume b < 5n.