Re: questions from a user ab. what determ. a puzzle's diffic
1. Programs can supposedly generate Sudoku that can be solved entirely by reasoning. Excepting the initial "solving" of cages to determine potential candidates for filling squares, is the same true for Calcodoku?
Not that I'm aware of.
2. How does the person running the calcudoku-creating software control "difficulty"? Are there multiple factors that can be individually manipulated, are is it a single factor varied along a particular range of values?
3. What is/are the factor(s)?
The most important factors are the cage size, and the operators used (subtraction is
more difficult than multiplication, for example).
4. If there are multiple factors, are any of them such that they can individually be recognized as some type of pattern by the solver in the end product?
Not sure I understand the question :-(
5. If there are multiple factors, is it possible to determine which are most "reliable" in creating a puzzle with the desired level of difficulty?
Maybe cage size distribution. If a certain distribution produces many puzzles with more than 1 solution, for example,
adding a few single cell cages typically quickly solves that.
After looking at "hard patterns" on the forum, a couple related questions. First, I assume that there is nothing inherently "difficult" about a pattern; one can create much easier puzzles, even for the "hard patterns". Maybe I'm wrong.
No, you're right, it's possible to create a trivial puzzle with a "hard pattern".
It's just harder (to create
), because it's less likely to occur.
But what about patterns of solution? The August 14 9x9 pattern seems to be "made" so that the middle row has to go first. While this might just be how I solve them, there seem to be common patterns with the 12x12's (a peripheral row/column--usually row is almost completely solved first)
This is maybe because of a shortcoming of the algorithm that generates the cages: when it
gets to the edges of a puzzle, it finds there's no space left for larger cages, so small cages
"bunch up" at the edge.
6. If these are "real" patterns, are they intended by the person running the software, a demonstrable function of the factors considered by that person, or how the software "interprets" its instructions?
Can you explain more?
7. If there are multiple factors, do particular factors result in particular patterns?
Not exactly answering this: the cage generator does a "random walk".
Finally, after doing puzzles on menneske.no (shapeless puzzles) it seems that the only "shape" factor I can identify is that, all else being equal, puzzles are easier if they have more cages that remain within a particular row/column. More cages containing lots of squares seem to make a puzzle harder if they cross multiple rows/columns, but easier if "linear".
Yes, I tend to agree: lots of interlocking creates lots of dependencies.
8. Are there particular patterns in cage "shape" that are definitely related to difficulty?
So probably anything covering more rows and columns (e.g. a zigzag pattern)
9. If so, is it intentional, a demonstrable function of the considered factors, or software "interpretation"?
I hope this make things a bit clearer :)