# The Islanders, Generalized

Logic Level 4

You have been marooned on an island with $n$ islanders total (including yourself). All of the islanders have the exact same weight, except for one person who weighs slightly more than everybody else. Your goal is to find that person.

The island has an old see-saw that can function as a makeshift scale: You can put some number of people on one side, and some number on the other, and the scale will either tip in the direction of the heavier side or balance. However, you want to use the see-saw as minimally as possible, since it is very rickety and could break.

What are the minimum numbers of balances needed for 10, 100, and 1000 islanders?