His clue density is three points lower than mine overall.įor all the puzzles with zero cells that lead to trivial ( Level-2) puzzles - I have tested them by inserting two clues. Klaus us searching for certain kinds of patterns and has steered his approach towards unsolvables whereas I have to wait for mine to pop out of general stock production, but I can see room for improvement. It is also a good sample set so I have worked out the chart.Ĥ6 out of 500 puzzles are 'zero' puzzles and the chart is nicely stacked to the left which I take to indicate a greater overall difficulty than my usual unsolvables. Klaus Brenner has been in contact with me a good deal recently and has supplied 500 puzzles currently 'unsolvable' on my solver and I'm honoured to publish some of these. The discussion also asked the question, are there any puzzles that require three or more cells to 'unlock'. If these puzzles do not have a single cell that leads to a trivial solution, perhaps two are required. These are number 4 (mine), number 29 (by Klaus Brenner) and number 28 and number 49 by David Filmer. The interesting puzzles are those with zero cells that lead to trivial puzzles. I will be withdrawing those unsolvables > 10 that have not been published so far. Unsolvable #61 has been panned as rather easy because it has 17 cells which lead to a trivial solution if these cells are known. The sample size here is not enough to draw any conclusions but those who have solved the unsolvables are able to distinguish the easier ones from the harder ones and I believe it is related to where they sit on the chart. I have elsewhere shown that the number of clues is not a major factor in determining the grade of a puzzle (it might prolong the experience which can cause a grade bump if the number of opportunities to solve in each 'round' is low) but I suspected that clue density would be a factor in this question, so I have coloured the graph to show it.
The unsolvable puzzles range in clue density from 22 to 30. This allows us to distinguish two puzzles of similar grade and may be a new metric for difficulty. If a puzzle has twenty different cells which all lead to a trivial solution then guessing (to throw in a quick strategy) will skip a bottleneck and the puzzle ought to be considered easier than a puzzle where no cell solution will render the puzzle trivial. However, the question is interesting as we can test a difficult puzzle for the number of Magic Cells that do render a puzzle trivial. The question is, are there any cells, which if filled in with a solution, would render the remaining puzzle trivial? That is, if I know the solution of cell X, would it allow us to skip all the advanced strategies? (Fariande is not alone in thinking about this approach and on the Player's Forum these cells are called Magic Cells, which I'll use from now on.)įariande offers a way to identify a Magic Cell but I'm not won over that it is a practical or satisfying strategy to use for solving difficult puzzles. All puzzles I grade as gentle, almost all moderate and some tough ones will be of this kind.įariande's approach is this: should a puzzle, using the solver, require more advanced strategies to continue we stop and look at the remaining uncompleted cells. I will define trivial as any puzzle that can be solved with these strategies alone. Fariande has posited the notion of Optimal Solutions Using Only The Basic Strategies 1-6 In the Solver, namely Singles, Pairs, Triples, Quads and Intersection Removal. This article pursues some interesting ideas being discussed on the Weekly Unsolvable Sudoku page.
A New Metric for Difficult Sudoku Puzzles?