At a school fair, you stumble across three children playing a game. The game involves four jars that each contain an equal number of marbles of each of six colors: blue, red, yellow, green, orange, and purple. In a turn, one draws a marble at random from each jar and the object of the game is to draw four marbles of the same color. The four marbles are then returned to their original jars and the turn ends. You observe each of the three children play a turn. The first child draws 2 green marble, 1 blue marbl, and 1 red marble. The second child draws 3 red marbles, and 1 yellow marble. The third child draws 4 blue marbles (and wins). In expectation, the third child has played M times as many rounds of this game as the second child has, and the second child has played N times as many rounds of this game as the first child has. Compute M+N.
