Question 3
Alvin and Bob take turns taking marbles from a bag. Alvin starts by taking one marble, then Bob takes two marbles, then Alvin takes three marbles, then Bob takes four marbles, and so on. If, during a turn, one of them doesn’t find enough marbles in the bag, then he takes all the marbles that are left. In the end, Alvin has $101$ marbles. How many marbles were in the bag at the beginning?