## What's wrong with XY-loops?

Advanced methods and approaches for solving Sudoku puzzles

### What's wrong with XY-loops?

Can someone translate to me what is being said here:

"One notable difference is that confirming loops, the almost nice loops yielding a clue, cannot be formed by XY chains. The links between bv cells must function as winks. If you have thought about the possibility of using the internal slink of the bv twice to confirm the starting candidate, as in the diagram below, forget it."
https://sysudoku.com/2012/03/06/xy-loops/

What does that mean in practice?? Does he mean by "confirming loops" discontinuous nice loops that have two strong links at the discontinuity? I'm assuming so. Let's look at an example:

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`.--------------.-----------.-----------.| 78   2    5  | 78  9  6  | 3   4  1  || 479  17   14 | 27  3  5  | 8   6  29 || 89   3    6  | 28  4  1  | 29  5  7  |:--------------+-----------+-----------:| 2    9    7  | 3   8  4  | 5   1  6  || 6    4    3  | 5   1  9  | 7   2  8  || 15   15   8  | 6   2  7  | 49  3  49 |:--------------+-----------+-----------:| 3    6    14 | 9   7  2  | 14  8  5  || 15   158  9  | 4   6  38 | 12  7  23 || 47   78   2  | 1   5  38 | 6   9  34 |'--------------'-----------'-----------'`

We're not interested in the obvious UR, or the normal XY-chains available. Instead, I'd like to know what's wrong (if anything) with these kinds of "confirming" XY-loops:

(8=7)r1c1 - (7=8)r1c4 - (8=2)r3c4 - (2=9)r3c7 - (9=4)r6c7 - (4=1)r7c7 - (1=4)r7c3 - (4=1)r2c3 - (1=7)r2c2 - (7=8)r1c1 => r1c1=8
(4=1)r2c3 - (1=7)r2c2 - (7=2)r2c4 - (2=9)r2c9 - (9=2)r3c7 - (2=1)r8c7 - (1=4)r7c7 - (4=1)r7c3 - (1=4)r2c3 => r2c3=4
(5=1)r6c2 - (1=5)r6c1 - (5=1)r8c1 - (1=2)r8c7 - (2=9)r3c7 - (9=2)r2c9 - (2=7)r2c4 - (7=1)r2c2 - (1=5)r6c2 => r6c2=5

They all yield correct results, but is there something fundamentally wrong with the logic (as the article seems to suggest) that I'm missing? I realize that I'm using the same strong link twice but does it matter? Is it just bad form or an actual flaw that might blow up in some other situation? Would it be more correct to write those same loops like this:

(7)r1c1 - (7=8)r1c4 - (8=2)r3c4 - (2=9)r3c6 - (9=4)r6c6 - (4=1)r7c7 - (1=4)r7c3 - (4=1)r2c3 - (1=7)r2c2 - (7)r1c1 => r1c1<>7 (=> r1c1=8)
(1)r2c3 - (1=7)r2c2 - (7=2)r2c4 - (2=9)r2c9 - (9=2)r3c7 - (2=1)r8c7 - (1=4)r7c7 - (4=1)r7c3 - (1)r2c3 => r2c3<>1 (=> r2c3=4)
(1)r6c2 - (1=5)r6c1 - (5=1)r8c1 - (1=2)r8c7 - (2=9)r3c7 - (9=2)r2c9 - (2=7)r2c4 - (7=1)r2c2 - (1)r6c2 => r6c2<>1 (=> r6c2=5)

In other words, are negative-proof discontinuous XY-loops ok (even though the notation partly hides their XY-nature)? I assume they must be per normal discontinuous Nice Loop rules. But, in that case the previous confirming logic must be true also because the discontinuity cell is a bivalue one. Therefore I'm assuming the real problem is just a formality (an illegally formed nice loop, perhaps?). Or, is the article talking about some entirely different situation and I'm missing the point?

More generally, I assume it's "illegal" to walk back in a nice loop, but does it actually break any logic if you do it near the end to return to the starting cell? I've been tempted to do that sometimes when I've started exploring a chain at some cell but the actual loop has formed elsewhere. In those cases I've played it safe and just used the smaller valid loop, but would be it terrible to walk back to the original starting cell using a few starting links backwards (imagine a loop with a tail)? I've never tried it and don't have an example at hand, but if I remember correctly, the inferences I thought I would get have worked out to be correct. Hardly necessary but is it possible if you really want a direct result in the original starting cell? I think the situation in the "confirming" XY-loop is similar, except the walk-back chain is just one link.

The article says: "Fortunately, quantum mechanics does not extend to Sudoku logic, and one candidate cannot be true and false at the same time." I guess I'm asking: why not?
-SpAce-: Show
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"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: What's wrong with XY-loops?

That's an author that refuses to partake In this forum, and has adapted and defined his own language for every thing he talks about it is rather frustrating to decifer exactly what he is referring to as non of it matches common diction found on any of the forums...

Took me months to just get him to drop his argument on my extended definition of a wxyz wing.. In the end I had to drop it and take his proclomating claim as defining something new... Ie bent almost restricted sets... Which already existed as als xz rule as over simplified. Derp...

Sadly I cannot help as his notations read off as subnet expansion chains validating a move.. Where I prefer reverse able logic constructs where math proves the question and answer.
Thay and he uses some weird color coded system and non standard cell notation. Onto of it.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1205
Joined: 05 September 2006

### Re: What's wrong with XY-loops?

StrmCkr, I hear you. I also have a hard time deciphering most of what he says (and draws), and I get frustrated if someone insists on using non-standard terminology. I'm still somewhat interested because I think he does have some useful ideas about manual solving. I don't like most of his implementations of those ideas, though.

Btw, is everyone else using software solvers nowadays, since I can't seem to find almost any other manual systems published? I'd be really interested in seeing how others solve non-trivial puzzles with just pencil-and-paper and what kind of mark-up they're using. I have my own extreme-capable system, but I'd like to know which parts of it are genuinely original and unique and which are unknowingly reinvented wheels. All I know for sure is that I haven't seen anything like it. Someone might also have ideas that I'd like to adopt.
-SpAce-: Show
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: What's wrong with XY-loops?

SpAce, I appreciate that you are just gathering ideas at the moment but here is a complete GEM mark-up which was started by only following conjugate links at first:

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` *----------------------*----------------------*----------------------* | 7‡8†   2      5      | 7†8‡   9      6      | 3      4      1      | | 4‡79‡  1†7‡   1‡4†   | 2†7‡   3      5      | 8      6      2‡9†   | | 8‡9†   3      6      | 2‡8†   4      1      | 2†9‡   5      7      | *----------------------*----------------------*----------------------* | 2      9      7      | 3      8      4      | 5      1      6      | | 6      4      3      | 5      1      9      | 7      2      8      | | 1†5‡   1‡5†   8      | 6      2      7      | 4‡9†   3      4†9‡   | *----------------------*----------------------*----------------------* | 3      6      1†4‡   | 9      7      2      | 1‡4†   8      5      | | 1‡5†   1!5‡8† 9      | 4      6      3†8‡   | 1†2‡   7      2†3‡   | | 4†7‡   7†8‡   2      | 1      5      3‡8†   | 6      9      3†4‡   | *----------------------*----------------------*----------------------*`

This shows a contradiction at r2c1 if the ‡ candidates are true, allowing this chain to be picked out.
(9)r2c1 = (9)r2c9 - (9=4)r6c9 - (4)r9c9 = (4)r9c1 => r2c1 <> 4 (making all the † candidates true).

This could also be presented at greater length as an X-Y chain but IMO that would require the reader to jump through extra circus hoops!

This particular grid has only two unsolved cells, r2c1 & r8c2, that are not bivalues. If every cell was a bivalue it would be called a Bivalue Universal Grave (BUG) as it would have 2 possible solutions. This pattern is therefore called a BUG+2. In at least one of the non-bivalue cells the true digit must be one that is not bilocal so there is a derived strong link (7)r2c1 = (1)r8c2 giving this chain:
(1)r8c2 =[BUG+2]= (7)r2c1 - (7=1)r2c2 => r6c2 <> 1 (=> r6c2 = 5)

This eliminates (5)r8c2 leaving r2c1 as the only non-bivalue cell so making the pattern a BUG+1 and proving r2c1 = 7.
I mention this because this route is much quicker to track.

The blogger you have been reading is a Microsoft Power Point afficiando and uses that in preference to a spreadsheet. However both approaches make it straightforward to keep the mark-ups up to date - the problem you are trying to overcome. My experiences with him are similar to StrmCkr's.

David
David P Bird
2010 Supporter

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Location: Middle England

### Re: What's wrong with XY-loops?

David, thanks, but I think you completely missed my point and question I'm asking a theoretical question about XY-loops and nothing else. This puzzle just happened to provide suitable examples. My question is still unanswered. Are XY-loops a valid concept or not? Apparently the concept itself was not invented by the Sysudoku guy as he says "Denis Berthier in his Hidden Logic of Sudoku, makes the statement that XY-loops are worthless."

Anyway, I'm not looking for the most efficient solution to this trivial puzzle. The most obvious one to me is the UR (15) at r68c12 (=> r8c2 = 8). Simple URs are boring, though, so I never use them if I can find something else. There's also the similarly obvious BUG+2, as you mentioned, and it's a bit more interesting to take advantage of (thanks for showing your way of using it!). I, however, wanted to hone my skills at finding XY-chains (a bit of a weak spot for me) and saw several opportunities here. That led to my question about those XY-loops or whatever they are.

Unfortunately this puzzle represents the most difficult level of my local newspaper sudokus, even though they're made by Arto Inkala himself. I use them for practicing intermediate techniques and I usually try to identify as many different solving methods as I can to get some fun and learning out of them. Otherwise they'd be too easy because there's usually one very obvious pattern. They could be easily solved with trial-and-error too (and I suspect most people do). GEM is definitely an overkill, so I refuse to use it for these.

The blogger you have been reading is a Microsoft Power Point afficiando and uses that in preference to a spreadsheet. However both approaches make it straightforward to keep the mark-ups up to date - the problem you are trying to overcome.

No, I'm not. My proprietary mark-up stays up to date very easily and reliably and needs neither Power Point nor Excel - just pencil-and-paper (not even colors needed) If I ever get tired of drawing by hand I'll code a real solver with the same functionality and graphics that I'm used to.
-SpAce-: Show
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: What's wrong with XY-loops?

SpAce, regarding XY chains and loops, you answered the question yourself - they are valid and will work but can take you the long way round to a deduction. Hence the jumping through hoops comment.

From your earlier thread I believed you wanted to tackle more difficult puzzles than those published in many papers, so I saw this as an opportunity to firstly show you the benefits of marking the conjugate inferences first when starting a GEM mark-up, and secondly to demonstrate how recognising a pattern could save a lot of effort once it is recognised. As soon as I saw the BUG, I never looked further and missed your UR!

All players have a common aim, to keep puzzles interesting by shunning certain approaches, but just where they set their boundaries depends on personal preferences which will usually change over time. It will be interesting to see where your boundaries end up.

For simple puzzles one challenge is to see how far you can progress without using pencil-marked candidates at all, just filling in the true digits in cells as you deduce them (Eleven is quite a master). However, it is the more difficult puzzles that will test the utility of your marking system.

Regarding Arto Inkala, I suggest you conduct a forum search on his name to learn more.

David
.
David P Bird
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### Re: What's wrong with XY-loops?

David P Bird wrote:SpAce, regarding XY chains and loops, you answered the question yourself - they are valid and will work but can take you the long way round to a deduction. Hence the jumping through hoops comment.

Ok. Thanks! As you should already know, I don't consider the jumping through hoops a problem when my motivation is to learn something or investigate a theory

From your earlier thread I believed you wanted to tackle more difficult puzzles than those published in many papers, so I saw this as an opportunity to firstly show you the benefits of marking the conjugate inferences first when starting a GEM mark-up,

I understand. It's just that when there are that many bilocation and bivalue links available, GEM is really a 3D-Medusa and it really doesn't matter where you start, right? It's also guaranteed to solve such puzzle without any thinking. It's a bit too omnipotent for my taste in such situations, even if used with your discipline

I think we should have a proper GEM discussion at some point and look at some more interesting examples. Since we last talked I've improved my method of applying it a bit. I moved GEM out of the main grid so I can use multiple seed points easily, and I also started using group markers which I considered useless before. I noticed the group markers can reveal some emerging locked sets, which actually makes them quite powerful. GEM really is a devastating weapon, but that's why I don't want to use it unless I have to.

and secondly to demonstrate how recognising a pattern could save a lot of effort once it is recognised. As soon as I saw the BUG, I never looked further and missed your UR!

My system makes them both quite hard to miss, which makes them boring. BUG+1, UR Type 1 and X-Wing are on my black list in these simple puzzles because they're too common, easiest to spot (in that order), and don't teach me anything. BUG+2 is just as easy to spot but a bit more interesting to apply, as you demonstrated.

All players have a common aim, to keep puzzles interesting by shunning certain approaches, but just where they set their boundaries depends on personal preferences which will usually change over time. It will be interesting to see where your boundaries end up.

I think they'll be constantly changing depending on the state of my bucket list. Learning is the fun part, and that's why I tend to avoid techniques I already feel confident about. I enjoy learning new techniques and practicing those I have difficulties with, even if they're not the most efficient tool for the job. Hence the voluntary jumping through hoops with XY-chains, too. They're simple in theory, but what makes them a bit harder for me in practice is that all links between cells are weak. For the same reason I'm not good at spotting wing patterns. X-chains and most AICs are much easier because they have lots of bilocation links that are readily visible in my mark-up.

There are also many techniques I haven't even added to my bucket list yet (JExocet, for example), so I don't expect to run out things to learn any time soon

For simple puzzles one challenge is to see how far you can progress without using pencil-marked candidates at all, just filling in the true digits in cells as you deduce them (Eleven is quite a master).

I do that as much as possible, although (and because) I'm not very good at it. If I applied my full mark-up on basic puzzles it would solve all but the hardest of them pretty much automatically, so there's not much point in that. For example, Arto's newspaper puzzles require only basic strategies on levels 1-4, and I solve all 1-3s and some 4s without pencil-marks. On 5s (like our sample) I always have to use some level of mark-up at the end.

However, it is the more difficult puzzles that will test the utility of your marking system.

Exactly. That's how my system has evolved as I've found its weaknesses when I've progressed to higher level puzzles. I'm actually pretty sure it's the most complete and powerful manual mark-up there is, but then again, I haven't really seen others so it's hardly an objective opinion Fortunately it has remained very scalable, meaning I can start with no or minimum mark-up and then add layers if the puzzle requires them. Applying the full mark-up takes a while, but it pays off with the extremes. Mix it with GEM and it's a weapon of mass destruction.

Regarding Arto Inkala, I suggest you conduct a forum search on his name to learn more.

Yeah, I kinda figured there's some bad blood. What should I conclude from that? My only point was that, whatever Arto's faults may be, he could obviously make much harder puzzles than the ones newspapers choose to publish. Even if his famous puzzles weren't actually quite as hard as he claimed, they were still pretty darn hard, right?
-SpAce-: Show
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: What's wrong with XY-loops?

SpAce, thanks for your response. The first thing I would like to say is please do not feel I'm insulting your intelligence when I go to lengths to describe something that you probably know already. I do this for the benefit of other readers following the topic who may not be so advanced (which, after all, is a purpose of a forum).

As I wrote before, I consider that you have embarked on a quite enjoyable and fulfilling path of discovery, and the last thing I want to do is to deprive you of the pleasure of making your own discoveries and decisions. So regarding your blacklist of methods, all I will say is that for the harder puzzles where strong links are scarce, you will find to make progress you will need to start bringing them into your repertoire. This is when you will need to decide how to rank their acceptability and consider what impact they may have your marking system.

The people that are not well received here are those that make exagerated claims and stubbonly stick to them when they are proved to be so, sometimes because there are commercial aspects.

You wrote: I have my own extreme-capable system, but I'd like to know which parts of it are genuinely original and unique and which are unknowingly reinvented wheels. All I know for sure is that I haven't seen anything like it. Someone might also have ideas that I'd like to adopt.
....
My proprietary mark-up stays up to date very easily and reliably

In that light, I find your choice of words worrying. Surely to say your system is "extreme-capable" is premature, and calling it a "propriety system" has commercial overtones. From the tone of what else you write, these phrases could just be result of your enthusiasm, but perhaps you would like to put my mind at rest.

David
.
David P Bird
2010 Supporter

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Location: Middle England

### Re: What's wrong with XY-loops?

David P Bird wrote:SpAce, thanks for your response. The first thing I would like to say is please do not feel I'm insulting your intelligence when I go to lengths to describe something that you probably know already. I do this for the benefit of other readers following the topic who may not be so advanced (which, after all, is a purpose of a forum).

Ok. That's a good reason, and I'm glad you stated it explicitly. You do realize that otherwise your style is possible to misinterpret?

So regarding your blacklist of methods, all I will say is that for the harder puzzles where strong links are scarce, you will find to make progress you will need to start bringing them into your repertoire. This is when you will need to decide how to rank their acceptability and consider what impact they may have your marking system.

That's a given, of course. We weren't talking about harder puzzles here, though. You said it yourself that people find ways to make simpler puzzles more interesting, and that's what I meant too.

The people that are not well received here are those that make exagerated claims and stubbonly stick to them when they are proved to be so, sometimes because there are commercial aspects.

Well, you don't know -- and can't know -- if my claims are exaggerated but you surely make a lot of assumptions. Why don't you ask me to show my system and then judge? Then again, you just made sure I no longer have any interest in sharing it here. It's kind of funny that I'm apparently the biggest (possibly only) fan of your favorite brain-child (GEM), but you're making every effort to belittle mine before you even know anything about it.

I also find it interesting that you've now made ad hominem attacks on three different people in one thread (first John Welch, then Arto Inkala, and now me). Are you perfect yourself, David? Personally I'm more interested in talking about sudoku than people's real or assumed character flaws. I like to consider ideas free from any biases and give credit where it's due, even if I don't particularly like the source or their style.

SpAce wrote: I have my own extreme-capable system, but I'd like to know which parts of it are genuinely original and unique and which are unknowingly reinvented wheels. All I know for sure is that I haven't seen anything like it. Someone might also have ideas that I'd like to adopt.
....
My proprietary mark-up stays up to date very easily and reliably

In that light, I find your choice of words worrying. Surely to say your system is "extreme-capable" is premature,

How exactly is it premature if I routinely use it to solve puzzles that are ranked "extreme" on standard scales? I consider my stable level at around 8.0 on the Sudoku Explainer scale at this time, and I haven't made any claims about neither my skills or my system beyond that. Mind you that I solved only basic puzzles until around May this year. How did I make that leap in a few months? By studying relevant techniques (mainly chaining because it seems to be the most versatile) and upgrading my system to support them. With my old system, or anything else I have seen, I couldn't have made that leap. So, I think it's fair to say that my system is "extreme-capable", or at least it has allowed me to be so. What's your exact counter-argument?

and calling it a "propriety system" has commercial overtones.

That was a poor choice of words of my part, even though I don't really know why it should bother you. By "proprietary" I meant that it's my own invention and probably quite unique in several aspects. Unfortunately I don't really know how it compares to other pencil-and-paper systems because I don't seem to find them published anywhere, and there appears to be little interest in that area anyway. If someone has better ideas I'll be sure to adopt them and give credit to the source, but it's hard to adopt something that doesn't seem to exist. The one thing I really hate is people stealing other people's ideas and presenting them as their own.

Still, I don't feel like I should be apologizing even if I did have commercial ambitions. What's wrong with those? Are you a commie who thinks it's somehow wrong to personally benefit from one's inventions??? Sorry if I don't empathize, even if I highly doubt that I will ever make a penny from mine. By all means tell me if you have ideas how to turn a manual sudoku mark-up system into riches!!! I'll surely give you a percentage if you make that happen.

From the tone of what else you write, these phrases could just be result of your enthusiasm, but perhaps you would like to put my mind at rest.

I don't find it necessary to put anyone's mind at rest. I'm not a big fan of rewarding patronizing and controlling attitudes that have no basis on reality or motives that I could understand. But don't you worry anyway. It's very unlikely that I would ever make or even attempt to make money on anything related to sudoku. However, I wouldn't surely mind or feel sorry about it if I did!
-SpAce-: Show
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: What's wrong with XY-loops?

SpAce, I think you are over-reacting to what I intended to be a gentle warning.

I'm sorry that you find my writing style pedantic, that was never my intention. Indeed I was keen to encourage you as fresh pair of eyes which would perhaps see things from new angles and might liven up the forum. Furthermore, you are a manual solver - it saddens me that the current membership is so computer-solver orientated.

I am not interested in getting involved in heated arguments. I'm now too old to care much.

David
David P Bird
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Location: Middle England

### Re: What's wrong with XY-loops?

SpAce wrote:... whatever Arto's faults may be ...

fyi, in 2006 Arto has generated the hardest known puzzle, i.e. the first one, which could not be rated by the former version of SudokuExplainer.
It took some days, that other such puzzles could be found by forum members, but the number of them then increased rapidly.
Years later (i think 2010 and 2012), Arto again claimed to have found the hardest puzzle(s) of the world, which was ridiculous, because 2010 hundreds, 2012 many thousands of harder puzzles were known. But the media believed him and this nonsense is still in the top results of a "hardest sudoku" search in the internet.

SpAce wrote:By all means tell me if you have ideas how to turn a manual sudoku mark-up system into riches!!!

[Edit: probaly only tens or hundreds at 2010/12]
[Edit2: in red after recherche]
Last edited by eleven on Thu Oct 05, 2017 3:55 pm, edited 2 times in total.
eleven

Posts: 2468
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### Re: What's wrong with XY-loops?

eleven wrote:fyi, in 2006 Arto has generated the hardest known puzzle, i.e. the first one, which could not be rated by the former version of SudokuExplainer.

That is not my recollection. Do you have a link to it?

Thanks,

Mike Metcalf

m_b_metcalf
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### Re: What's wrong with XY-loops?

It is mentioned in the top post of the thread The hardest sudokus.
eleven

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### Re: What's wrong with XY-loops?

First of all, I want to make clear that I don't know Arto and have no reason to defend him. In fact I hate liars and frauds, so if someone can prove he's in that group, I have very little sympathy. I'm just a little puzzled (pun intended) that there's so much whining about his claim to fame but apparently no one has tried to set the record straight in the media.

It seems to me that originally Arto seized the moment and made a name for himself because no one else had bothered to do the same. Who can blame him? Apparently he didn't actually lie in his first claim either, even if his puzzle was the hardest for only a short time. Is it possible that the harder puzzles started appearing only because of his media fame and no one was really interested in producing them before? If that's the case then I see no problem with his first claim. The later claims seem more bothersome, if in fact a bunch of harder puzzles had already been published and he should have known it.

So, who *really* has the goods?
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"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

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### Re: What's wrong with XY-loops?

Hi,

This pdf file link contains Top 10 puzzles created by Finnish applied mathematician, Dr. Arto Inkala.

R. Jamil
rjamil

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Joined: 15 October 2014
Location: Karachi, Pakistan

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