You are given two identical plastic balls, which you can drop from various floors of a building to carry out your experiment. If a ball doesn't break after being dropped, it may be reused without suffering any loss of quality. But if both balls break before you have reached the highest floor, then the experiment is a failure. What is the least number of times you must drop the balls in order to reach the highest floor?

The answer is 14. You drop the first plastic ball from the 14^th floor. If it breaks, then you can determine the highest floor by dropping the plastic ball no more than 13 times (drop it from the 1^st floor, and if it doesn't break, drop it from the 2^nd floor, and if it still doesn't break, drop from the 3^rd, etc). If the first ball survives the drop from the 14^th floor, you then drop it from the 27^th floor (14 + 13 = 27). If it breaks, you can complete your test in no more than 12 drops with the second ball by dropping it between the floors 15 to 26. If from the 27^th floor, the first ball still doesn't break, the next floor to drop it from is the 39^th (14 + 13 + 12 = 39). If it breaks, drop the second ball from floors 28 to 38 (max 11 drops). Repeat the experiment the same way whenever the first ball doesn't break; after the 39^th floor should be the 50^th floor (14 + 13 + 12 + 11), then the 60^th floor (14 + 13 + 12 + 11 + 10), and so on. If the first ball survives 11 drops, you will be on the 99^th floor. In that case, it only takes one more drop to complete the whole test.