1. There are 100 doors in a row, all doors are initially closed. A person walks through all doors multiple times and toggle (if open then close, if close then open) them in following way: In first walk, the person toggles every door In second walk, the person toggles every second door, i.e., 2nd, 4th, 6th, 8th, … In third walk, the person toggles every third door, i.e. 3rd, 6th, 9th, … ……… ………. In 100th walk, the person toggles 100th door. Which doors are open in the end?

2. There are two empty bowls in a room. You have 50 white balls and 50 black balls. After you place the balls in the bowls, a random ball will be picked from a random bowl. Distribute the balls (all of them) into the bowls to maximize the chance of picking a white ball.