Creating the Grading Scale

A good standard grading scale would run from 0 to 10. Because mankind operates in a base 10 world, this scale just plain makes sense. The largest factor in determining whether or not an individual can solve a puzzle is whether the individual knows enough strategies to solve it. If one does not know the strategy, one cannot apply it, and the Sudoku cannot be solved. For this reason, allocate 7 of the 10 points in the grading scale to strategic difficulty. A 7 will be given when the program does not have enough strategies in its arsenal to solve the puzzle. Otherwise, the puzzle will assume the strategic difficulty score of the most difficult strategy it uses. A 6 will be granted if X-Wing or Swordfish are used. A 5 will be granted if Hidden Quads are used, as they can be extremely difficult to spot. A four will be given if a Naked Quad, Hidden Triple, or Hidden Pair is used. A three will be given to Naked Pairs and Naked Triples. Naked subsets are quicker to spot than hidden subsets, thus a Naked Subset the same size as a Hidden Subset will have a lower score. Finally, a two will be given if Locked Candidates are used, a one if Hidden Singles or Singles are used, and a zero if only Slicing and Slotting and Simple Singles are used. These last two strategies are quick to spot and do not require keeping candidate lists, and thus carry the lowest difficulty rank. With strategic difficulty assigned, now the program can assign procedural difficulty scores.

A procedural difficulty score is more difficult to assign because individuals solve puzzles in different ways and tend to take different paths when approaching the same Sudoku puzzle. That said, there are a couple of universal factors that will make a puzzle procedurally difficult. First is the number of candidate elimination strategies used. If the bulk of strategies used to solve a puzzle do not result in any values being placed, an individual solving the Sudoku will have a much harder time. So if more than four candidate elimination techniques are used, one can add one to the procedural difficulty score. If eight are used, the puzzle is especially difficult, and another procedural difficulty point can be tacked on. The second problem that will make a puzzle procedurally difficult is its sheer length. This can be measured by counting the number of empty squares in the puzzle. If there are more than 55 squares to solve, a final procedural difficulty point may be added. This results in a total possible procedural difficulty score of 3, which adding to the strategic difficulty score, will give a score out of 10. The grading scale is complete

Posted in Sudoku Grading Theory at April 26th, 2009. Trackback URI: trackback

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