Coin Weighing with Interval Queries

In the classical coin weighing problem, we are given a row of n coins, some of which may be counterfeit. Weighing any subset of coins tells us how many genuine coins are present in that subset. The goal is to figure out exactly which coins are counterfeit using as few weighings as possible. But keeping track of all the coins with arbitrary subsets can be confusing! In this work, we restrict ourselves to only weighing subsets that are continuous intervals. We will discuss the number of weighings required in three regimes: non-adaptive, adaptive average case and adaptive worst case.