We prove the following results on enumerating or counting furthest pairs given an ultrametric space with n elements:
• There is a deterministic O(F + nlogn)-time algorithm for enumerating all furthest pairs, where F denotes the total number of furthest pairs.
• There is a Monte Carlo O(n/ε 2 )-time algorithm that estimates the number of furthest pairs to within a multiplicative factor in (1−ε,1+ε), where ε > 0. Furthermore, the time complexity of O(n/ε 2 ) cannot be improved to o(n · f(ε)) for any f(·).