Livingston is a marble freak and loves to play at school. during the first break he doubled the number of marbles he had. during the second break he lost four marbles (no big deal). during the third break, he increased his stock of marbles by 1/3. during lunch, however, he lost half of his marbles. after school, livingston played again and tripled what he had. he went home with 72 marbles. how many did he start with?

He went home with 72 marbles after tripling his stock. That means he had 72/3 = 24 before school ended. 

If he lost half at lunch, he had 24 * 2 = 48 before lunch. 

During the third break, he increased he stock by 1/3. That means that 48 = 4/3 * x, so he had 36 before the third break. 

During the second break he lost 4, so before he had 36 + 4 = 40. 

During the first break he doubled his marbles, so before he had 40 / 2 = 20.