Kropki

Rules and Tips for standard puzzle types, and their variants

Kropki

Postby nickdeller » Wed 08 Dec, 2010 11:46 pm

I'm putting this in the Sudoku section initially as the rules can be applied to a sudoku variant; I suspect the consensus will be to move it to general Puzzles, though. Rules are adapted from the current standard rules in the Classic Sudoku thread, n is the size of the grid.

    Place a number from 1 to n in each empty cell. (One number per cell.)
    Each row and column should contain each number from 1 to n.
    When consecutive numbers appear in a pair of cells which share an edge, that edge is always marked with a white circle.
    When one number in a pair of cells which share an edge is exactly double the other, that edge is always marked with a black circle
    In the event that 1 and 2 appear in a pair of cells which share an edge, the circle marking that edge may be either black OR white.
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Re: Kropki

Postby detuned » Sun 12 Dec, 2010 10:57 pm

I'd vote this to go in with the puzzles. Kropki sudoku can then be described as a kropki, with the extra sudoku constraints.
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Re: Kropki

Postby drsteve » Wed 12 Jan, 2011 7:45 pm

detuned wrote:I'd vote this to go in with the puzzles. Kropki sudoku can then be described as a kropki, with the extra sudoku constraints.


Personally, I see it as a sudoku with additional Kropki rules. Splitting hairs, but I'd say a Kropki Sudoku comes under Sudoku
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Re: Kropki

Postby ronaldx » Wed 12 Jan, 2011 10:56 pm

By the consensus definition, anything with third constraint is a sudoku variant...?

Kropki doesn't apply third constraint to all cells, so isn't a sudoku variant by that definition, if we accept that.
Kropki sudoku does apply third constraint to all cells, so is a sudoku variant


Kropki itself is so sudoku-ish (if I had to describe it to a friend, I would start with "it's like sudoku but...") that maybe it just needs to be listed twice ;)
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Re: Kropki

Postby sknight » Mon 14 Feb, 2011 12:11 pm

I wouldn't put Kropki in with the Sudoku variants. The issue for me is that there are a lot of puzzles that have the basic "magic square" format, and many of them don't really feel like Sudoku to me. For example, is Skyscrapers a Sudoku variant? You're arranging the numbers from 1 to N so that they don't repeat in the columns and rows, just like Kropki, but doesn't feel like Sudoku to me. Ken Ken? Seems closer to Sudoku (enough that it gets called Calcudoku when people don't want to risk trademark issues by calling it Ken Ken). But what is it that makes Skyscrapers less Sudoku-ish and Ken Ken more so -- its not just that the numbers are on the outside because Outside Sudoku variants are perfectly viable and still feel like Sudoku.

I tend to agree that that third contraint on the numbers is necessary for something to be called a proper Sudoku variant. That's the difference between Killer Sudoku and "addition only Ken Ken".
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Re: Kropki

Postby drsteve » Mon 14 Feb, 2011 4:27 pm

I think Kenken feels like sudoku because it is so close to Killer Sudoku.

I think though that Calcudoku tends to include the third constraint - it's basically a Killer with four operations. I might be mistaken though.

Ah, just checked Gareth's magazine and he doesn't include the third constraint. Surely just changing the name wouldn't affect the copyright though. Either it's a KenKen or it's not because the rules are different.
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Re: Kropki

Postby ronaldx » Mon 14 Feb, 2011 5:29 pm

Surely just changing the name wouldn't affect the copyright though. Either it's a KenKen or it's not because the rules are different


I might be wrong about this but I think the name 'KenKen' is trademarked. I don't think you can copyright the concept of a puzzle? Although perhaps you can copyright individual instances?

Ah yes: http://www.conceptispuzzles.com/index.a ... o/news/285
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Re: Kropki

Postby drsteve » Tue 15 Feb, 2011 8:19 am

ronaldx wrote:
Surely just changing the name wouldn't affect the copyright though. Either it's a KenKen or it's not because the rules are different


I might be wrong about this but I think the name 'KenKen' is trademarked. I don't think you can copyright the concept of a puzzle? Although perhaps you can copyright individual instances?

Ah yes: http://www.conceptispuzzles.com/index.a ... o/news/285


Does Calcudoku include the possibility of more than 2 numbers in a subtract or divide "box"? That might be implied given the "based on the rules of Kenken" rather than "exactly the same rules as Kenken". It seems rather unfair that if I created the world-breaking BattleBarge puzzles, that involved, say, L-shaped battleships, and copyrighted it, then someone could produce a puzzle with exactly the same rules under the name, say, BattleStewart.

Oh, I'm claiming that one, by the way. BattleBarge puzzles - copyright me!
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Re: Kropki

Postby ronaldx » Tue 15 Feb, 2011 4:28 pm

I think you can trademark a name, assuming certain conditions, and you have to apply for a trademark of the word you want to use - which has to not otherwise be used in the context of puzzles and the trademark is considered by a jury and as such has to be paid for.

You have automatic (free) copyright over anything you written - so a written version of the rules would be under your copyright. And the design of an example puzzle would be under your copyright.

However, the concept of the puzzle I don't think is copyrightable. So, as long as I rewrite your rules (BattleBarge) in my own terms (BattleStewart), that's fair game. That's how I understand copyright law to work.

I think perhaps you might be able to *patent* the idea of a puzzle. However getting a patent would be egregious (cost of a 10-year european-patent is estimated €32000), and you shouldn't distribute the puzzle in the public domain until after you had applied for the patent, in every region you wanted the patent to apply. But I'm not sure if patents would even apply to pen-and-paper puzzles - it would be more likely to apply to something physical (http://www.sudoku-ball.com/index.php?op ... &Itemid=31).
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Re: Kropki

Postby drsteve » Tue 15 Feb, 2011 6:05 pm

I suppose it would be virtually impossible to police and not exactly economicaly to take to court, so I guess there will probably never be a defining answer to this question.

Still, I'll be miffed if the Battlebarge idea gets nicked...
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Re: Kropki

Postby detuned » Tue 15 Feb, 2011 6:43 pm

Both Kropki and KenKen (or whatever) or indeed skyscrapers are Latin square puzzles. You can add the 3x3 box constraint to any of these if you like, but at their most basic they remain puzzles I'd definitely not call sudoku.

If you ask me, any form of copyrighting or trademarking puzzles beyond individual pieces of work is stupid and counter-productive, and the day concepts/rules of puzzles become the property of any individual is the day puzzling dies. See as a particularly potent example the mockery Thomas Snyder made of KenKen on his blog.
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Re: Kropki

Postby motris » Wed 16 Feb, 2011 12:29 am

[puts on puzzle wonk hat]
Two points:

First, all these discussions of where to put puzzles in a hierarchy strike me as failing by using sudoku as a touchstone. While this is a convenient choice as sudoku is one of the most recognized (and misrecognized) logic puzzles these days - sudoku seems synonymous with puzzle in some circles - it is well zoomed in on the broad puzzle landscape already. So the fact almost no other puzzle qualifies as a sudoku, but many puzzles can be turned into sudoku forms, seems missing here when the discussion turns to whether a thing (say Kropki) is a sudoku or not.

In the broad hierarchy of puzzles, there are puzzles that should be classified as symbol placement puzzles (as opposed to things like path/loop-forming puzzles, a similarly broad category that would get mazes and Slitherlink and Numberlink and such, or observational puzzles or manipulative puzzles and perhaps a few other groups). Within symbol placement puzzles are puzzles that literally just use symbols (like Star Battle) but also more meaningful symbols such as word and number-based subgenres. Some of those puzzles would be things like word fill-ins and Fillomino that have different types of logical rules but no specific geometric uniqueness constraints. There are also symbol placement puzzles that have these unique group constraints, of which Latin square puzzles are the most common. Within this family, Kropki, Calcu-doku, Skyscrapers, even Easy as ABC puzzles belong. That some take numbers and others letters is a problem if we are overly strict in how we classify things. A subset of Latin square puzzles, with a third unique group constraint based on regions, are Sudoku. Without the third constraint - specifically a region-based third constraint - you do not have a sudoku in my opinion. A calcu-doku has a third constraint (based on sums/products/... of cages), but this is not a region-based constraint and therefore not a sudoku. It feels close, because it is close, but it is not an exact cousin of a sudoku.

I feel there is a job for some Linnaeus of puzzles to formalize this a bit more with kingdom and phylum all the way down to genus and species, but I'd call Sudoku a "Symbol-placement number-based puzzle with three-way uniqueness constraints on each cell". A typical Kropki puzzle is a "Symbol-placement number-based puzzle with two-way (Latin square) uniqueness constraints on each cell as well as numeric property-based constraints between pairs of cells". A Kropki sudoku merely changes two-way to three-way in the above, but until it does so it is not a sudoku. Certainly more closely related as a puzzle to a sudoku than a spot the differences to a sudoku as it belongs in the symbol-placement kingdom, number-based phylum, and similar uniqueness-group class, but no more a sudoku than a chimp is a human for all its genetic similarities.

That's the last I think I'll write here about this. It seems each new entry in the sudoku forum re-inspires this debate until the topic ends up being moved to "puzzle". But that seems the correct motion in every case. Unless you do mean "symbol placement" or "number-based" or "unique element constraints" to always stand for sudoku. Then just be clear about that fact.


Second, and more interesting conversationally, with the concept of trademarking/patenting a puzzle, certainly someone can protect the trade name of their product. Within Japan, Sudoku cannot be used by anyone other than Nikoli. Nikoli did not seek world-wide protection on this name though, so it is free to use outside of Japan by any publisher. Everyone, from Shortz to me, can call their puzzles Sudoku. No one else calls their's "wordless crossword puzzles" - and this does not help the puzzle hierarchy section above if sudoku is suddenly a subtype of crossword puzzles - but I could imagine St. Martin's could have some trade protection on that marketing terminology which is strictly that - marketing terminology.

Nextoy has taken the steps to trademark KENKEN and KenDoku and are the official suppliers of that name/brand of puzzle, but not that type of puzzle. They do not and cannot claim exclusive rights on Latin square puzzles involving arithmetic. First off, they would have a heck of a time proving they had "invented" the concept in the mid 2000s considering decades of prior published puzzles. If such minor changes count as new ideas, then my using multi-cell subtraction already would qualify as a further "new" design and wouldn't be a problem anyway. Second, as mentioned up-thread, "concepts" are harder to protect than tangible objects. So individual puzzles/books cannot be copied, but derivative (or improved) work in the same style is allowed. Hence, things like TomTom Puzzles.

A gray area exists though when it comes to puzzle presentation itself. Last year, after a breakdown of a relationship between the Grabarchuk family and Conceptis puzzles, the product Strimko was released as Chain Sudoku with identical presentation (sets of circles, lines, and colors) which extend beyond the rules of the puzzle itself. Here, I think legally Conceptis is in the clear, but morally they ripped off another product and design to release their own version, particularly considering the state of discussions that I'm aware of between the parties before this release. Look for the story to become the basis of The Social Network 2 if it ever becomes a billion dollar product.

So, when I write puzzles - realizing I am often making new types and borrowing other's types, I do my best to give credit when I am taking an idea and don't mind when others take styles I have developed and use them for their own designs. I do care when you steal my puzzles, or reprint them without using my name. Admittedly some of my work is now in the public domain, such as WSC example puzzles, but still when an authorship or credit can be provided it is worth giving that credit if known. And hoping for anything more than credit when an idea is used or stolen by someone else is simply not reasonable given the ubiquity of new puzzle evolution in public locations.
[/takes off puzzle wonk hat]
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Re: Kropki

Postby apollo1001 » Sat 29 Sep, 2012 4:57 pm

Ignoring the above discussion on what type of puzzle this is, I would be more interested in some tips for this puzzle type. Having seen my first of these only a few moments ago on croco-puzzle, I was more than a little flummoxed for about 15 minutes on how to even start! After this time, I had deduced 3 things:

1. On a 1-8 grid, the numbers 5 & 7 will never have a black circle next to them.
2. Consecutive white circles (in a straight line) must form a consecutive number chain.
3. 2 consecutive black circles force the centre to be either 2 or 4.

A bit of trial and error then found me the correct sequence to get started on the bottom row, and I worked my way up the puzzle. I'll probably look for some more of these and experiment further, but would welcome other's starting points on these...
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Re: Kropki

Postby nickdeller » Sat 29 Sep, 2012 6:08 pm

apollo1001 wrote:Ignoring the above discussion on what type of puzzle this is, I would be more interested in some tips for this puzzle type. Having seen my first of these only a few moments ago on croco-puzzle, I was more than a little flummoxed for about 15 minutes on how to even start! After this time, I had deduced 3 things:

1. On a 1-8 grid, the numbers 5 & 7 will never have a black circle next to them.
2. Consecutive white circles (in a straight line) must form a consecutive number chain.
3. 2 consecutive black circles force the centre to be either 2 or 4.

A bit of trial and error then found me the correct sequence to get started on the bottom row, and I worked my way up the puzzle. I'll probably look for some more of these and experiment further, but would welcome other's starting points on these...


An important thing - and I don't think we've mentioned it anywhere as a specific tip - is that "no circle" is meaningful! For example, a no circle neighbour of 4 in a 1-8 grid can only be 1, 6 or 7.
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Re: Kropki

Postby sknight » Sun 30 Sep, 2012 2:43 pm

Apollo:
The Kropki the other day that you tried is definitely a tricky place to start, and it sounds like you figured out a lot of the important things.
I wouldn't say I'm particularly good at them, but just to give some general feel for the genre:

Kropki typically vary in size from about 6x6 to 9x9, with 7x7 being a pretty common easier size.
You are correct to focus on the "doubles" and "can't be doubles" in the pattern.
Notice that in 6x6, you can easily run into situations where you can find the 5 in a row/column because only one square
isn't attached to a black dot. And in both 6x6 and 7x7, then any 3-square runs of black dots must have a 2 in the middle with 1/4 on the sides.
Also in 6x6 and 7x7 if you have two black dot pairs in a row/column, one is a 3/6 and the other is from the 2^n family.
More generally, it is definitely often possible even in 9x9 puzzles to segregate your black dots into "3/6" vs "2^n" families.
The numbers on the ends of the spectrum (1 and N) are constrained by the fact that they have only one consecutive number.
Large numbers of white dots tend to give you a lot of information about parity, and this can sometimes also connect to the fact
that 1 and 3 are the only odd "black dot" numbers.
In nasty Kropki, filling in candidate numbers (pencil marks) can help brute force things if you're stuck.
But, really, one of the nice things about Kropki as a puzzle is often the "break" consists of some interesting new configuration of
information (a cluster of dotted squares) that you haven't necessarily encountered before, but which forces something in a creative way.
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Re: Kropki

Postby apollo1001 » Tue 02 Oct, 2012 5:33 pm

Many thanks to you both - time to practise :P
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