Dropping Balls Puzzle - Solution

The Puzzle:

Dropping Balls
You have to do an experiment to determine the highest floor on a 100-floor building from which a manufactured snooker ball may be dropped without breaking.

You are given two identical snooker balls, which you can drop from various floors of the 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 determined the highest floor, then you are an incompetent bungler and your boss is ultimately going to fire you.

What is the least number of times you must drop the snooker balls in order to determine the highest floor?

Our Solution:

The answer is: 14

You drop the first snooker ball from the 14th floor. If it breaks, you can then determine the highest floor by dropping the second snooker ball no more than 13 times (drop it from the 1st floor, and if it doesn't break, drop it from the 2nd floor, and if it still doesn't break, drop from the 3rd, etc).

If the first ball survives the drop from the 14th floor, you then drop it from the 27th 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 27th floor the first ball still doesn't break, the next floor to drop it from is the 39th (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 39th floor should be the 50th floor (14+13+12+11), then the 60th floor (14+13+12+11+10), and so on. If the first ball survives 11 drops, you will be on the 99th floor. In that case, it only takes one more drop to complete the whole test.

(Puzzle and solution courtesy of JaneFairfax)
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