Ruud wrote:ronk wrote:I'm of the impression that the "magic candidate" would be the candidate eliminated causing [8,5]=8, also via the simplest of constraints (naked or hidden single).

When looking for the optimal solving path, I used the term "magic candidate" for the candidates that forced a complete solution. Since there can be only one per cell, the term "magic cell" is equally valid.

What you're proposing here is that any single candidate that, when eliminated, forces a magic cell to it's solution digit is in itself a "magic candidate".

I apologize for my prior flippant comment, so let me explain my thinking.

I believe there are two categories of magic cells or magic candidates: one category for those interested in solutions by a human solver, or a computer program that emulates a human solver, and another category for those interested in computer-based solutions.

Without really realizing it earlier, most likely because of our earlier discussion on the Optimal Solving Path thread, I was thinking of a definition that would be appropriate for a human solver. The logical human solver is able to make cell assignments only as a result of, or in conjunction with, elimination of candidates.

At any given state of the puzzle, there might be several possible eliminations from which to choose, depending upon the skill and patience of the human solver. In this context, and in the context of an optimal solving path, finding an elimination that leads to a solution via singles only ... as early as possible ... seems like a reasonable basis for the definition of magic candidate.

For computer-based solutions, the objective of finding one (or more) magic candidate(s) that can be assigned in one (or more) magic cell(s) is different. Here we are interested in the assignment of a magic value at a magic location, at a time when candidate elimination is likely not available to cause that assignment.