ELECTING NEIL :

The response for this is, of course. In this case, we considered the point of the search or researching is to find an artifact  -  a word which is an anagram of "electing neil" or we can say its other specified name. So no one really cares in which order to actually arrange and again re-arrange the letters, so we are not searching for a path. 

• Completeness

It's also worth trying to estimate the number of solutions to manipulate the problem just like it, and the density and the maximum range of those solutions amongst the non-solutions. In a search or researching any kind of problem, then there may be any number of solutions that have given, and the problem's explanation may be or not involve finding just one but it depends on our given data, finding some, or finding all the solutions. For example, suppose a military application searches for ways and points that an enemy might take. The question is there that: "Can the enemy got from A to B" requires finding only one solution, while as the question: "How many ways to uses for the enemy catch from A to B" will require the agent to find all the solutions of our question.

When an agent is asked to find just one solution, so we can just program it to prune its search space quite heavily, i.e., rule out exacting operators at particular period to be more efficient. When ever, this may be prune some of the solutions of our problem, so if our agent is asked to find all of them, the pruning has to be under controlled so that we knew that pruned areas of the search space either contains no solutions, or may contains solutions which are duplicated in another (non-pruned) part of the space.