Consistent and Admissible Heuristics

Question

Any consistent heuristic is also admissible. But when is a heuristic admissible but not consistent (monotone)?

Please provide an example in which this is the case.

Answer 1

Long dead, but I'll give my two cents anyway. I think by far the easiest way to think of this is that an admissible heuristic says that you can't overshoot when getting to a particular defined goal node, while a consistent heuristic says that you can't overshoot when getting to ANY node. This makes the relationships clear: since the goal node is some node, a consistent heuristic is admissible. But since admissible only guarantees this property for one node, admissible does not imply consistency.