The problem gets more interesting if you have 3 balls, 4 balls, etc. I believe
for 3 balls, n = 100, the first floor should be 36. 8 * 9 / 2!, max 8 tries for 4 balls, n = 100, the first floor should be 56. 6 * 7 * 8 / 3! max 6 tries for 5 balls, n = 100, the first floor should be 70. 5 * 6 * 7 * 8 / 4! max 5 tries