Pour Water Between Buckets to Make Water Levels Equal

Given several buckets with fixed capacities and initial water volumes, determine whether (and if required, the minimum number of pours) you can make all buckets contain the same amount by repeatedly pouring from one bucket to another until the source is empty or the target is full. The core challenge is exploring the state space (or applying invariants like total water and gcd-based reachability) to test feasibility and optimality.