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?
