Puzzle decorations

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Fred76
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Puzzle decorations

Post by Fred76 » Fri 11 Jan, 2019 10:59 pm

Sometimes puzzles are not what they seem to be.
For example in round 6 of WSC 2016, an extra-regions was presented as killer sudoku, a windoku as renban sudoku, a diagonal sudoku as pointing different, etc... that's due to the meeting of variant rules on some points (a 9 cells killer cage is an extra-region, etc...). That's fine.

If you look at the tournament unlucky 13 which happened in 2015 on LMI (it was a kind of april fool's tournament): http://logicmastersindia.com/lmitests/?test=M201504S, you'll see that all puzzle are presented as sudoku variations, but all sudoku were classic sudoku (or at least equivalent to classic sudoku). For example, we have some sudoku with extra-regions and all digits in those extra-regions are given. Or a thermo-sudoku with all digits given on the thermometers. That's fine, too.
If I have to write the definition of classic sudoku, then I would see from the rules of the puzzles of the tournament unlucky 13 that the puzzles are not classic sudoku. But the actual puzzles are classic sudoku, because the variations things are just decorations, and you don't need variant rules to solve the puzzles.
My question is then: How much is it a sacrifice to renounce to useless decorations if we have to write a definition and if the decorations and useless rules are outside the defintion?

The 2 examples above have no such issue because everything is about sudoku (in my opinion), so the twist doesn't create a problem. But imagine someone organize a classic sudoku tournament. As an author, I would not give him the puzzles of tournament unlucky 13 (without removing the variation decorations), because rules are confusing and can't be labeled as classic sudoku rules.

I feel this phenomenon appeared to a lesser extent in WSC 2017 round "Is it a sudoku?" where some rules were really only decorative.
The kind of message I understood is that some people don't want a strict definition of sudoku, just because they want to be free to add useless decorations to their puzzles (in that case, the goal was to make a WPC round with same puzzle types as WSC round). Thus my question above: are we ready to renounce to useless decorations?

Fred

detuned
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Re: Puzzle decorations

Post by detuned » Sat 12 Jan, 2019 5:00 pm

I'm not sure I understand the question fully - as I don't think what you are describing is much of an issue. As far as I can tell, you are concerned about people being confused by rules which are redundant to solving the puzzle. But as far as I can tell, it's only on very rare occasions that a puzzle then fails to require the use of those rules. The example you posted is a case in point - as an April Fool's concept it is by design supposed to be a bit silly. Anyhow, insofar as this might be a problem, I think this is more a question about good puzzle design than it is about definitions.

However, to twist your idea around, it might be interesting to think about whether it is possible for a given variation to be presented equivalently as sudoku. This tends to rule out any such decorations which come with the caveat that "all possible decorations" are given - which means the absence of the decoration is equally (if not more so) meaningful to solving the puzzle than the decorations themselves.

As I've stated elsewhere, I have no problem with Renban appearing as Windoku, and Killer as Extra Regions. Quite the contrary, I think it is a very useful way to help guide a classification of additional constraints and decorations you can give to Sudoku.

Fred76
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Re: Puzzle decorations

Post by Fred76 » Thu 14 Feb, 2019 12:08 pm

detuned wrote:
Sat 12 Jan, 2019 5:00 pm
I'm not sure I understand the question fully - as I don't think what you are describing is much of an issue. As far as I can tell, you are concerned about people being confused by rules which are redundant to solving the puzzle.
It's not so much the question of confusion than the fact that this confusion could be about rules that should not appear in a category of puzzle. And even more important: the fact that these decorations would prevent to write a defition for a category of puzzle (see the other thread for a complementary discussion: viewtopic.php?f=33&t=1937&p=15001#p15001).

I would take few other examples.

If I say "placing pentominoes is not something we should allow for a puzzle to be labeled as sudoku variation".
What kind of things someone may answer is: "We can create a puzzle containing rules about placing pentominoes, but in the puzzle itself it will not be relevant, it'll be only a decoration, or trivial enough so that players are not bothered by it. Thus it is stupid to forbid puzzle containing pentomino rules from sudoku variation".
What I think is that, if these things add only trivial things, that is not a loss to forbid them. I don't understand why some people feel so negative about forbidding something which is futile.

The point is not to forbid all decorations, the point is to not let these decorations prevent to write a definition. If a decoration is allowed by definition, it's ok, but if a decoration is not allowed by the definition, it's not ok.

Fred

Fred76
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Re: Puzzle decorations

Post by Fred76 » Thu 14 Feb, 2019 12:37 pm

Here is a concrete example.
I would like to make analogy of this situation with classic suoku, because I assume we all know the definition of classic sudoku.
I would not qualify a thermo-sudoku as classic sudoku. I would not qualify killer sudoku as classic sudoku. Both of these variants contain rules which make them not belong to the category of classic sudoku.

Here are 3 puzzles:

1. Classic sudoku
classique2.png
classique2.png (19.74 KiB) Viewed 4409 times
2. Thermo-sudoku
thermo.png
thermo.png (19.89 KiB) Viewed 4409 times
3. Killer sudoku
killer.png
killer.png (18.9 KiB) Viewed 4409 times
Both thermo-sudoku and killer sudoku are quasi identical to the classic sudoku.
Should we change the definition of classic sudoku to allow these 2 puzzles to belong to the category of classic sudoku?
or can we have an agreement about the fact that only the first one is a classic sudoku, and the 2 others are not classic sudoku, despite the fact they are quasi identical; and forbidding them in a classic sudoku competition (replacing by the first one) is not something which is horrible?

Fred

Nilz
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Re: Puzzle decorations

Post by Nilz » Thu 14 Feb, 2019 7:29 pm

The top one is a classic sudoku. The bottom two are not, although they are obviously very close.
(One difference is that the top example works just as well with the numbers replaced by unordered symbols, whereas the others don't).
I think part of the reason in my head that it's not an analogous situation to the overall question is that defining the rules for a single example of puzzle is different to defining the rules for a class of puzzles, if that makes any sense?

--------------------------
I think the rest of this comment is just a bunch of rambling nonsense, but I'm going to leave it there in case it means anything to anyone!
--------------------------

I guess the point is to show that in some situations you can have puzzles that are almost identical yet sit on opposite sides of the line. But the difference in my view (and sorry to get a bit mathsy) is that classic sudoku is like a closed ball, in the sense that it has a fixed border, whereas the concept of sudoku as a whole is more like an open ball (with the closed ball inside it), where one can get arbitrarily close on either side of the border, because there is no real border.
I've probably explained that very badly, apologies. The other thing I don't like is that as the complement of an open set is closed, by my own logic one could simply define exactly what is 'not' a sudoku, instead.
In conclusion, this comment is a badly explained mash-up of different ideas and you should probably ignore it, but if you've read this far and can explain what's going on in my head, please try. :-)

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Re: Puzzle decorations

Post by detuned » Thu 14 Feb, 2019 8:18 pm

My initial reaction to those 3 examples is similar to Neil. The bottom two are definitely not classic sudoku. The fact that they are very similar to classic is due to the fact that the constraints used resolve themselves trivially, leaving the rest of the puzzle as an exercise in filling in the classic. That to me is less a question of identity and more a question of poor puzzle design (in this case of course I acknowledge you are making a very specific point rather than to create a good puzzle). The reason I say this is because there are other variants where you tend to solve the constraint, and then you are left with a classic left to solve - in other words the solving of the puzzle is separated when it comes to the constraints. A good example of such a variant might be Star Product Sudoku.

I think this highlights why it might be more fruitful to try and classify constraints, rather than classify variants. Of course the two concepts are very similar, but if you start talking about variants then you do get in to this discussion where constraints have been used in poorly designed or even trivial ways.

I think to try and make your point even better than you did, I would give you the example of Killer with only single cell cages. I think that probably would count as classic sudoku, albeit poorly present classic sudoku. Still, I don't think my approach in this case would be to ban all single cell cages from killer as a matter of definition. I think it's more like a style guide in that you probably shouldn't have single cell cages, but there may be some occasions, perhaps with a specific theme, where exceptions could be made.

detuned
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Re: Puzzle decorations

Post by detuned » Thu 14 Feb, 2019 8:21 pm

Neil: I very much enjoyed your fumbling around with topological ideas :)

I think there is definitely something to be said for defining what a Sudoku is definitely not (or indeed defining some red lines for puzzles that should be appearing at competitions). The difficulty lies in being entirely comprehensive, and so what I envisage is that at the end of this process we will have two lists of things that a sudoku or a sudoku variant definitely should be, and things that it definitely should not be.

Fred76
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Re: Puzzle decorations

Post by Fred76 » Fri 15 Feb, 2019 10:07 am

Nilz wrote:
Thu 14 Feb, 2019 7:29 pm

--------------------------
I think the rest of this comment is just a bunch of rambling nonsense, but I'm going to leave it there in case it means anything to anyone!
--------------------------

I guess the point is to show that in some situations you can have puzzles that are almost identical yet sit on opposite sides of the line. But the difference in my view (and sorry to get a bit mathsy) is that classic sudoku is like a closed ball, in the sense that it has a fixed border, whereas the concept of sudoku as a whole is more like an open ball (with the closed ball inside it), where one can get arbitrarily close on either side of the border, because there is no real border.
I've probably explained that very badly, apologies. The other thing I don't like is that as the complement of an open set is closed, by my own logic one could simply define exactly what is 'not' a sudoku, instead.
In conclusion, this comment is a badly explained mash-up of different ideas and you should probably ignore it, but if you've read this far and can explain what's going on in my head, please try. :-)
--------------------------
Well, I think I've seen things that are more nonsensical than that.
Correct me if the things I say are not right, my knowledge in topology goes back more than 20 years ago...

1. It's anecdotic, but if I'm not mistaken, a complement of an open can be open, too (perhaps it reassure you).
2. I think I get your idea that the set of sudoku variations is an open set. To me, it doesn't mean that we can't define it. A lot of mathematical open set are well defined.
3. The fact that we are always able to create a puzzle which is just slightly different and is still inside the open set doesn't mean that every puzzle that are slightly different from a sudoku variation is a sudoku variation. It could be that your tiny change is just too big. If you consider the open set A=]0;1[, and say that the operation y=x+10^(-100) is a tiny change, there are some x so that x∈A, but y∉A.
4. It could exist a closed set which is just slightly bigger and contains the open set you describe as the set of sudoku variations, it's ok for me to say the closed set is the set of sudoku variations (if we take the analogy of A=]0;1[, if really it is an issue to have an open set, we can just chose the set B=[0;1], it is fine).
--------------------------

Fred

Nilz
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Re: Puzzle decorations

Post by Nilz » Sat 16 Feb, 2019 12:34 pm

Is point 1 true? I can't remember enough from my uni days frustratingly!
Can't find flaw in points 2-4 though.

detuned
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Re: Puzzle decorations

Post by detuned » Sat 16 Feb, 2019 7:31 pm

Nilz wrote:
Sat 16 Feb, 2019 12:34 pm
Is point 1 true? I can't remember enough from my uni days frustratingly!
Can't find flaw in points 2-4 though.
At the risk of going waaaay off topic, yes: https://en.wikipedia.org/wiki/Clopen_set. Somewhat trivially, the empty set and the entire space are always both open and closed. In general the concept of being both closed and open is a good way to capture a notion of discreteness. To bring things back on topic, we might by analogy view the space of all puzzles as a topological space. There are many different topologies you might give to any space, but our task is to come up with some kind of rules or definitions (or a topology in our analogy) so that we end up with a discrete subspace of Sudoku. As I've hinted at before, there is no definitive way of doing this - there could be several ways of doing it to one degree or another.

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