Allow creation of harder puzzles.

Programs which generate, solve, and analyze Sudoku puzzles

Allow creation of harder puzzles.

Postby tso » Wed Jun 22, 2005 6:22 pm

I'd like to be able to create harder "challenge" puzzles -- the type that currently the software will recognize and solve, but labels arguably unfair, and will not create.

When I dub a puzzle in, I want to be able to distinguish between puzzles it calls invalid -- those that have unique solutions that cannot (as far as we know) be reached without trial and error -- and those that are *truly* invalid that have no solution or mulitple solutions. And of course, I want to be able to actually load in these types of puzzles.

Further, I'd like to be able to create puzzles that DO require trial and error, as they're hard to find elsewhere. (Maybe there's a better word than invalid -- it's confusing. No dictionary definition or thesaurus entry supports this use of the word.) Solving this type of a puzzle is a different experience than solving the other types -- just as solving an easy, medium or hard puzzle usually gives you a different experience. Each tends to require different techniques. Easy -- you might use a pen to enter the numbers directly. Medium, you might use a few pencil marks in several cells. Hard, you might fill ALL the cells with each possble number in pencil marks. Challenge (those requiring Trial and Error), you might print out two more more copies of the puzzle or use the branching capability in the program. I find each experience different and enjoyable, depending on how much time I have, my mood, etc. I guess I understand why you don't want the software to create this kind of puzzle -- if the newspapers that use the software publish this type, especially without a proper warning, it could turn some people off which could reflect badly on the software. Still, if there was some 'easter egg' type of hidden menu, or if a warning was displayed and/or printed with puzzles of this type -- people don't have to try them if they don't want to. (I personally NEVER do 16x16 puzzles, having tried a few times. They're just to tedious for me and I ALWAYS make a clerical error that spoils it. Having them in the menu doesn't inconvenience me at all.)

Speaking of invalid puzzles, I'd like to be able to create a puzzle that has, lets say, exactly 2 solutions -- the challenge being to find BOTH of them. Puzzles like this are impossible to find. (I once solved a group of 5 puzzles -- they weren't Sudoku -- in which the instructions were that one had NO solution, one had MULTIPLE solutions. You had to solve the three that were valid and identify the other two as no solution and mulitple solution. THAT was hard.)

I'd like to have the option of specifing the number of clues given.

I'd like to be able to use the software to create a puzzle from scratch, step by step, with the software keeping me informed of the current validity and difficulty rating of the puzzle entered so far -- multiple solutions, no solution, valid, easy, hard, etc.

I'd like to be able to create variant Sudokos, especially those with irregular sub-groups, like this one:

Code: Select all
| 7 | .   3   .   6   .   .   . | . |
|   |   +---+-------------------+   |
| . | 9 | . | .   .   4   .   .   2 |
|   |   |   |   +---+---+-----------+
| 8 | . | . | . | . | . | .   .   . |
|   +---+   |   |   |   +-------+   |
| . | .   . | 6 | . | .   .   2 | . |
|   |   +---+---+   +-------+   |   |
| 9 | . | .   2   .   8   . | . | 3 |
|   |   +-------+   +---+---+   |   |
| . | 2   .   . | . | 5 | .   . | . |
|   +-------+   |   |   |   +---+   |
| .   .   . | . | . | . | . | . | 4 |
+-----------+---+---+   |   |   |   |
| 1   .   .   4   .   . | . | 3 | . |
|   +-------------------+---+   |   |
| . | .   .   .   7   .   4   . | 6 |

(each row, column and fenced off area has all nine digits)

Ideally, I'd like to draw the fenced areas myself. A randomized pattern of 'corrals' would be good as well.

I'd like to be able to create puzzles that consist of overlapping 9x9 (or 6x6, etc) puzzles, though that sounds like more than just a tweak or an add-on, but a major project unto itself. Still, they are fun to solve and have no greater complexity to solve than a single puzzle -- they just take longer.

I'm sure you've seen more variations than we have when you were researching this. If there are variations that can't easily be put into the software, you might want to put some on the website with a URL only registered owners would have ...

When dubbing, I'd like to be able to choose the cell with the arrow keys and enter the digit with the keyboard. This option is available for SOLVING, but does not work for dubbing, when it would be FAR more useful. Dubbing by the current method is slow and annoying.

For all this, I'd gladly pay triple the current price!
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how about a 3D version?

Postby AULKpuzzler » Thu Jun 23, 2005 1:56 pm

Is it even possible:?:

:idea:A 3d cube. 9 cells down, 9 cells across, 9 cells deep. If it is possible, this would be a fun puzzle to complete.

Might be graphicaly challenging to create though.:(
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Re: how about a 3D version?

Postby scrose » Thu Jun 23, 2005 2:02 pm

AULKpuzzler wrote:Is it even possible? A 3d cube.

It's possible, although the one example I have seen wasn't a very satisfying puzzle to solve.
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Postby Karyobin » Tue Jun 28, 2005 3:35 pm

It is, of course, important to sleep occasionally.
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Postby scrose » Wed Jun 29, 2005 2:49 pm

There have been a requests in the past (1) (2) asking for harder puzzles or easing the restraints about invalid puzzles. Wayne has stated that he doesn't want his program to validate or produce unfair puzzles. Even so, I will offer a feature for consideration.

Suppose there is a setting in the Game Options that allows a user to put the program into Expert Mode. While in Expert Mode, the gloves come off, all restrictions are removed: puzzles can be created that require swordfish, colouring, forcing chains, nishio, trial-and-error, you name it; unfair and invalid puzzles can be dubbed in without receiving errors or warnings; puzzles with irregular block shapes are supported; the sky is the limit...

When a user switches to Expert Mode, they would receive a warning explaining of the possible terrors that await them. Or perhaps the Expert Mode would be available only in a separate version of the Pappocom software. This separate version could have a higher price tag and no support would be offered to those who buy it: use at your own risk!
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Postby Hammerite » Wed Jun 29, 2005 4:13 pm

Wayne is foolish if he insists on limiting the functionality of his software. There are already free tools available on the Internet which offer functionality not included in his paid-for software. If he ends up losing out on sales because he thinks certain puzzles should not be supported (on fairly flimsy grounds) then he will have only himself to blame.
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Postby tso » Wed Jun 29, 2005 9:25 pm

Hammerite wrote:Wayne is foolish if he insists on limiting the functionality of his software. There are already free tools available on the Internet which offer functionality not included in his paid-for software. If he ends up losing out on sales because he thinks certain puzzles should not be supported (on fairly flimsy grounds) then he will have only himself to blame.

I'm with you, though he might not lose much in sales. I'm guessing that part of his choice is to separate his software and puzzles from the rest of the world's. That could be why he uses words like "arguably unfair" rather than something like "extremely difficult" and the complelety confusing and inaccurate "invalid" for the harder ones instead of "Beware -- really darn hard, no really, I mean it, you can't do it -- I dares ya". I think he may believe -- and he may well be correct -- that if his software created the hardest types of puzzles, newspapers would publish them and the majority of people who came across them would NOT like them and actually cost him sales as well has adversely effect the popularity of the puzzle in general.

As a non-programmer, at first I assumed that it would be easier to create the hardest puzzles and that the problem would be to sort out the easier ones, but I've heard from more than one programmer the reverse may be true. So it may be that he isn't so much limiting the functionallity -- it may be that it is beyond his software's capability an would require changing the method by which it creates new puzzles -- and why would he do that if he sincerely doesn't like that type of puzzle?

Actually, I've got to give it up to him for completely sticking to his guns. Most people are more interested in giving the public what they ask for instead of being true to themselves and creating what they really like. But I still hope he'll change his opinion.

I completely disagree with with him that "arguably unfair" and "invalid" puzzles are less fun to solve. He cannot speak for everyone. Personally, I find them the MOST fun to solve. He said: "there's no way a (non-superhuman) human can solve an Unfair puzzle without writing pencilmarks everywhere and doing a lot of tedious, time-consuming, mechanical plotting of numbers - which is no longer fun." -- I am obviosly NOT superhuman, and yet I do solve them. I don't know what he means about time-consuming, mechanical plotting -- doesn't EVERYONE use pencil-marks already in hard puzzles? (Come to think of it, arent ALL Sudoku's just time-consuming, mechanical plotting of numbers?) The line he's drawing is invisible and arbitrary. It is NOT possible to give an definitive description of which puzzles are human solvable and which are not, and certainly not which ones are fun or not. (And why *does* he have branching capability if he's anti-t&e? Or "undo" for that matter. If enabling us to more easily use t&e, might as well allow us to create or dub in puzzles that he thinks require it.)

He sidesteps the issue of "invalid" completely -- as if they were, in fact, invalid. If a Sudoku has a unique answer, it's valid. If I construct a large enough Sudoku, maybe 100x100, it would not be solvable by humans and probably not solvable by the largest computers in a billion years -- the puzzle would still be valid, just unsolvable. This is the case for ALL NP-complete puzzles.

The world is filled with puzzles that can only be solved with trial and error. Sliding block puzzles and Sokoban, for example have been very popular over the years and ultimately must be solved by trial and error. Both are actually P-space complete -- even more complex than mere NP-complete.
Who would claim that they are "invalid?"


Popular pencil puzzles more in the same genre as Sudoku, such as Minesweeper and Battleship are also NP complete. When solving the hardest Battleship puzzles, one is expected to make proofs by contradiction. The popular FATHOM IT program, which creates Battleship puzzles, includes a step by step logical solver that shows demonstrates this on the expert level puzzles. (The author's puzzle appear regularly in GAMES magazine and in many of the International Puzzle competitions.) By Wayne's definition, the expert level puzzles would be labeled as "invalid".


That being said, he is correct when he says that Nikoli and the other Japanese Number Place magazines rarely if ever publish puzzles that his software would rate as "arguably unfair" or "invalid". I've tested the hardest puzzles in a dozen magazines and I couldn't find anything above a "hard". I can guess three reasons for this: 1) Their target audience isn't brainiacs and "super-humans", it just people who want to relax and do a puzzle, writing directly into the magazine or book, in relatively small sized grids. I don't know the demographics -- but that might shed some light on it. 2) The magazines come out 6 to 12 times a year with 150 to 200 puzzles. If some are so hard that they take hours and hours to crack -- maybe customers would need to buy them so often. 3) Japanese puzzles are made by hand. The methods to creating a puzzle are similar to solving one in reverse. It may be very difficult to create -- or next to impossible -- to create the hardest types of "invalid" puzzles this way -- and it may not even occur to the puzzle creators to do so. They've been making them this way for 25 years -- they were probably NOT computer checking them for solvability at first, so all the puzzles had to be solved in advance by hand as well. It is more difficult to solve a puzzle and confirm that it has one and only one solution that it is to merely solve a puzzle that you KNOW has one and only one solution, if that puzzle is in the "arguably unfair" or "invalid" category of complexity, in some cases, substatially more difficult.

As a solver, I can attest that often, solving an "invalid" puzzle is often very enjoyable. For me, the best part, the part I look forward to, is when half the puzzle is done and half the cells have only two possiblities. It is at this point, one may be able to -- using only one's eyes -- follow the connections from one cell to another -- if this, then this, then this, etc. -- sometimes for dozens of if/thens -- until you see it -- this cell MUST be this, not that. This doesn't require any special skills, super-human or otherwise. It doesn't usually require looking for or finding a contradiction. (Yes it can be time consuming. If I didn't have the time, I wouldn't be solving a puzzle.) It's certainly no more tedious than many of the other techniques required to solve hard puzzles.

Wayne also said somewhere that if the solver uses Trial and Error, then a very hard puzzle is no harder than a hard puzzle. But the same can be said for most other solving tactics -- if you choose not to use a specific tactic, the puzzle you're working on will be more difficult to solve! Many people choose to avoid using pencil marks or use as few as possible -- knowing that if they use more, the puzzle will be too easily solved. (I suppose if one chooses to use ONLY trial and error -- no pencil marks, no cross hatching, etc -- even the easiest puzzle becomes difficult.)

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