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questions from a user ab. what determ. a puzzle's difficulty
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Posted on: Fri Aug 17, 2012 12:06 pm

Posts: 2238
Joined: Thu May 12, 2011 11:58 pm
questions from a user ab. what determ. a puzzle's difficulty
I got this as an e-mail from a user, but he/she wrote that it'd be fine to put it on the forum:

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Some questions from a person with no math background beyond a basic calculus course 20+ years ago and no computer background. And I don't read tips or solving "techniques". So these may not even be the "right" questions. Also, to make up for my unfamiliarity with necessary vocabulary, I promise to make this extra wordy.

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?

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)?

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?

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?

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.
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) and, with the August 15 6x6 difficult pattern, the first "real" deduction sees a single number narrowed down to one of two spots in two columns (rectangle of R1 and 6, columns 2 and 3 (or columns 4 and 5)). There may be others.

Which got me wonderin':

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?

7. If there are multiple factors, do particular factors result in particular patterns?

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". But that's based on observation and the very general idea that puzzles are easier when you can narrow things down more during the initial calculations.

8. Are there particular patterns in cage "shape" that are definitely related to difficulty?

9. If so, is it intentional, a demonstrable function of the considered factors, or software "interpretation"?

I certainly don't expect you to answer all of these. (I'd be happy if you can understand what I'm trying to ask!) But maybe you can tell me where someone (without math/computer experience) can look into this stuff.

Many thanks,

StarCannibal
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Posted on: Fri Aug 17, 2012 12:15 pm

Posts: 2238
Joined: Thu May 12, 2011 11:58 pm
Re: questions from a user ab. what determ. a puzzle's diffic
starcannibal wrote:
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.
starcannibal wrote:
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).
starcannibal wrote:
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 :-(
starcannibal wrote:
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.
starcannibal wrote:
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.
starcannibal wrote:
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.
starcannibal wrote:
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?
starcannibal wrote:
7. If there are multiple factors, do particular factors result in particular patterns?

Not exactly answering this: the cage generator does a "random walk".
starcannibal wrote:
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.
starcannibal wrote:
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)
starcannibal wrote:
9. If so, is it intentional, a demonstrable function of the considered factors, or software "interpretation"?

?

I hope this make things a bit clearer :)

Patrick

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