2022 SSMO Team Round Problems/Problem 14

Problem

On a hot summer day, three little piggies decide to play with water balloons. The three piggies travel to a 200-floor parking garage each armed with exactly one water balloon.

The game works as follows:

• If a piggie drops a water balloon from any floor of the building, it will either break, or it will survive the fall.
• If the water balloon breaks, then any greater fall would have broken it as well.
• If the water balloon survives, then it would have survived any lesser fall.
• Every water balloon is identical and interchangeable.

The goal for the piggies is to find the lowest floor that will break a water balloon. Assuming they play optimally, what is the minimum number of tries in which they are guaranteed to find the lowest balloon-breaking floor?