The New Sudoku Players' Forum

[SpAce]

The only part I disagreed with is calling it continuous,

Well, that was a pretty significant part in this discussion, I think Anyway, do you now agree that according to the standard Nice Loop definitions it [X-Wing] can be called continuous [X-Cycle]? It may not be continuous by *your* definition but that's hardly a good argument if you're the only one using that particular definition (whatever it is -- it's still unclear to me). I think "continuous" and "discontinuous" are pretty well defined and generally understood in the standard Nice Loop context (which also applies to X-Cycles). By those definitions X-Wing is clearly a continuous loop (an even number of nodes, all alternating inferences without breaks, after the eliminations only strong links left, etc).

As it clashes with my perception and understanding of what makes it a full connected loop thus continuous, nothing further needs to be discussed on that as I cannot make my perception any clearer then I tried. I am also not here to change your mind either. Attempt to show case what I perceive as a continuous loop. And that's it.

I can accept that. However, I still can't understand what your idea of a continuous loop is. I'm sure you have done everything you can to explain it to me, so no need to redo it. I'll go over what you've written and see if I can catch what you really mean. I'll get back to you when I do... or when I catch the bug in your thinking

I also quoted another site that also calls it continuous in quotes that agrees with you with same point of view,

Yes, but I don't consider SudokuWiki an authoritative source on the theory and practice of all techniques, so I wanted to link another one that I personally respect more with regards to Nice Loops specifically. I don't mean to bash SudokuWiki at all as it was very helpful when I started studying advanced techniques, but since then I've learned that not all information there is quite accurate or complete (see this recent thread, for example: http://forum.enjoysudoku.com/continuous-loops-with-als-nodes-t34306.html). For a beginner it's a good starting point, though, and the online solver is very easy to use (it's one of the three I use to check gradings and alternate solutions, besides SE and Hodoku).

also i am probably the only one with an odd definition difference between the word and usage of continuous/ discontinuous

It's usually not a good idea to have multiple definitions for the same words in the same context. If your understanding of "continuous" and "discontinuous" is different from the de facto standard Nice Loop definitions, then it might be a good idea to use different words (and define them clearly) to avoid misunderstandings. Alternatively you could make a compelling argument for the whole community to accept your new definitions. Sorry about the lecturing, but this kind of avoidable confusion is exactly one of those issues that I've been criticizing about the sudoku terminology. Let's not add to the problem if we can avoid it. My general preferences would be:

1) No multiple definitions for the same term in the same context
2) No multiple names for the same concept in the same context

i will agree hodoku has flaws and bugs too. {it is a very solid solver in any regards}, some stuff needs updated to enhance it further and add the missing conditions on some techniques to expand their eliminations further.

I agree that at least the information on the Hodoku site seems quite good. It's been one of my two main sources for learning about chains and loops (the other one being the previously mentioned Paul Stephens' Nice Loop tutorial) and also other stuff. I haven't really used the solver itself for anything except to check its gradings and solve paths (after I've completed a sudoku on paper), but it does seem quite capable. That's why I'm surprised if it can't show X-Wing as a continuous loop. I'm inclined to think it's an omission or a bug (though one that has zero practical impact).

[StrmCkr]

Last attempt

B = A - C = D - B = A

would be the expressed chain as a continous loop as both a and b see each other as start and end points

More over , it also shows it isn't a continuous loop of any kind as a x cycle cannot re use cells with same candidate . To circumstances vent that
Both authors use a weak link at start and strong link at the end, ie invisible invalid links by their own construct rules.
Ie.
a-c=d-b
Or
c-a=b-d
Are the valid elimination chains seen by a fish /x cycle. Both being disconious.

Also to note x chain and x cycle are the same in hodoku as he defines x chain as a turbot, which a turbot is a fish cycle

That is also quoted in both links provided, and is the reason hodoku and several other solvers will never find the continous forum you are saying it is.

What it does with out the extra a&b cells listed it can show and implies implies A = D or B = C
what can be interpreted from that is that any cell that sees A C may be eliminated and any cells the see B & D can be eliminated

Which is an elimination rule missing in hodoku.

Ps this is also why there is two elimination chains per Xwing as a chain.

scranraid information is based on the link you provided most of its a direct edited copy.

[SpAce]

It seems that you're right that Hodoku really can't see X-Wings as continuous loops of any kind. That's weird -- but like I said, it doesn't prove anything except that even Hodoku has its limitations. On the other hand, the SudokuWiki solver sees X-Wings both as Continuous X-Cycles and generic Continuous AIC Nice Loops, just the way it should. That's exactly how Hodoku should work, too, but it doesn't.

In fact, it seems that Hodoku has no such concept as X-Cycles at all (only X-Chains), which partly explains the problem. It should still catch X-Wings as Continuous AIC Nice Loops, but it doesn't do that either. So, I think we found a bug in the mighty Hodoku, just like I suspected. Since we're talking about X-Wings, I think it's appropriate to quote Darth Vader here: "Don’t be too proud of this technological terror you’ve constructed. The ability to destroy a planet is insignificant next to the power of the Force." In other words, it's not a good idea to blindly trust software if its results are in conflict with Logic.

I think I also found a related bug in your argument:

X-cycles as a turbot requires 2 moves to prove all the x-wing eliminations, these chains are bi directional as the end points{elimination cells} are also used in the chain!!

Turbot Fish: 2 r2c2 =2= r8c2 -2- r8c8 =2= r2c8 => r2c1345679<>2
Turbot Fish: 2 r8c8 =2= r2c8 -2- r2c2 =2= r8c2 => r8c1345679<>2

seen as an x-cycle requires 2 moves to prove all the x-wing eliminations, these chains are bi directional as the end points{elimination cells} are also used in the chain!!
X-Chain: 2 r2c2 =2= r8c2 -2- r8c8 =2= r2c8 => r2c1345679<>2
X-Chain: 2 r8c2 =2= r2c2 -2- r2c8 =2= r8c8 => r8c1345679<>2

it can also be an AIC requires 2 moves to prove all the x-wing eliminations, these chains are bi directional as the end points{elimination cells} are also used in the chain!!
AIC: 2 2- r2c2 =2= r8c2 -2- r8c8 =2= r2c8 -2 => r2c1345679<>2
AIC: 2 2- r8c2 =2= r2c2 -2- r2c8 =2= r8c8 -2 => r8c1345679<>2

See what I mean? You're assuming that Hodoku treats it as an X-Cycle but it doesn't! It only sees X-Chains which do require two moves (one for each chain) as they should. The Turbot Fish and the AIC are just the same chain with a different name, and thus they also require two moves. For some reason Hodoku doesn't see the X-Wing as a loop of any kind like it should. It doesn't mean it's not a loop. It most certainly is.

[StrmCkr]

Turbot are fish cycles of lenght 5. X chains are defined by hodoku as a turbot.

They are one and the same, see my post above to y it won't ever find it.

They also start on a strong link and end on a strong link, noting that they cannot rescue same digit cells.

Which gives it a minimal lenght of 4

[SpAce]

Turbot are fish cycles of lenght 5. X chains are defined by hodoku as a turbot.

No. You got that wrong too. X-Chain is a generic (any length) single-digit chain. Turbot fishes are special cases (length 4) of that.

"A Turbot Fish is an X-Chain that is exactly four candidates long."

http://hodoku.sourceforge.net/en/tech_sdp.php#tf

[SpAce]

Also to note x chain and x cycle are the same in hodoku as he defines x chain as a turbot, which a turbot is a fish cycle

That's wrong too. Turbot is not a fish cycle. Cycles are loops, Turbots are chains.

Edit: Of course Turbots like any X-Chains can be loops (X-Cycles) too, but they're special cases. X-Wing is such a special case, and a continuous one too. Not all Turbots or other X-Chains are loops. For example, Skyscraper is a Turbot but not an X-Cycle, though it can be broken into two discontinuous ones. 2-String Kite is a Turbot that can be seen as a discontinuous X-Cycle if you include the elimination cell (then its length can be seen as 5, but it's not really part of the Turbot pattern).

[StrmCkr]

http://sudopedia.enjoysudoku.com/Turbot_Fish.html

[StrmCkr]

How about, we make a thread and title
the ultimate chain guide.

make a single guide that drops all this back and forth that covers singles, naked, hidden links, grouped, bi-local,eri, odd even length, bivalve. Strong and weak inferences, als, ahs within chains.

[SpAce]

http://sudopedia.enjoysudoku.com/Turbot_Fish.html

To me the Sudopedia definition looks very old and not very useful compared to the Hodoku one. Note that it's not showing all of Skyscraper's eliminations which are only possible (in one step) if you see it as a chain and not a loop. If you treat it as a loop you'll need two moves for its eliminations.

It's a good thing you brought that conflicting definition up, though! Another source of confusion registered. It seems that one needs to provide a reference to any definition used in sudoku discussions, or there's a chance that people are using different ones and not understanding each other.

[SpAce]

How about, we make a thread and title the ultimate chain guide. make a single guide that drops all this back and forth that covers singles, naked, hidden links, grouped, bilocal, odd even lenght, bivavle. Strong and weak inferences, als, ahs with in chains.

Not a bad idea. Don't you think we need to agree on some basics first? This is a good discussion, though. I didn't even realize how many different definitions there are for certain things. It's hard to find common ground if people are talking about different things but using the same names for them.

[StrmCkr]

There you go, a clear example of progression in history of solving
cycles are chains, considering peers of start and end applies to both and enhances eliminations.

Older definitions didn't do this instead they proved the start as false
Via odd lenght loops, the skyscraper would need 4 loops to show all eliminations instead of 1 move.
Tedious at best.

[StrmCkr]

Not a bad idea. Don't you think we need to agree on some basics first? This is a good discussion, though. I didn't even realize how many different definitions there are for certain things. It's hard to find common ground if people are talking about different things but using the same names for them.

We have agreed on alot of stuff already and have common ground

No cell can be reused in chain notation on same digit. (as it can't be both true and false at the same time)

Chain any lenght any digit any type of node.

Loop any lenght any digit any type of node
Defined as a loop as this:
Where first cell and last cell share one common digit and are direct peers, so that last point assertion of candidate y directly implies first point as x, which intern triggers the chain of events that prove y is true on last point.
x at the first spot places y in the last cell. Via the chain (not directly)

[SpAce]

Via odd lenght loops, the skyscraper would need 4 loops to show all eliminations instead of 1 move.

You're technically right. I said two moves because it's possible to cut some corners even if you use discontinuous nice loops: the elimination cells in both boxes can be considered groups and thus start/end nodes for the chains. That leaves you with two moves. I no longer start/end my chains with the elimination cell(s), but I still did when I started this thread. You can see that style in my original solution steps in the first post. Every step is a discontinuous nice loop that starts and ends with the elimination cell(s). In step 4 I had a Discontinuous Grouped X-Cycle that eliminated two candidates:

Hidden Text: Show

Code: Select all

+---------------+----------------------+----------------+
| 4   267 279   | 5       1679    16e9 | 19    3   8    |
| 5   89  3     | 149     189     2    | 149   7   6    |
| 68  67  1     | 347fa-9 367fa-9 68e9 | 2     45b9 45  |
+---------------+----------------------+----------------+
| 2   1   4579  | 6       589     58d9 | 4579  45c9 3   |
| 3   89  59    | 2       4       7    | 589   6   1    |
| 68  467 4579  | 19      159     3    | 45789 2   457  |
+---------------+----------------------+----------------+
| 9   24  8     | 137     12357   15   | 6     145 457  |
| 7   5   24    | 8       126     16   | 3     14  9    |
| 1   3   6     | 79      579     4    | 57    8   2    |
+---------------+----------------------+----------------+

Originally I notated it like this:

(9): r3c45-r3c8=r4c8-r4c6=r13c6-r3c45 => r3c45 <> 9

It starts with a group node, hence two eliminations with one move. (With a normal Skyscraper you could do that twice to get all eliminations.)

Now I would simply do it with this X-Chain (Grouped Skyscraper):

(9)r3c8=r4c8-r4c6=(9)r13c6 => -9 r3c45

(which incidentally looks exactly like Leren's step 3). Makes no practical difference here, but with a normal Skyscraper it would save one move.

[eleven]

No cell can be reused in chain notation on same digit. (as it can't be both true and false at the same time)

Sorry, i didn't follow the whole discussion, but this looks strange to me.
What about a chain 1r1c12=...=1r1c123 => -1r1c4-9. Isn't this reusing 1 in r1c12 ?

[StrmCkr]

but this looks strange to me.

mind putting a picture to your context? as the ... cells don't tell me jack about what it is some random numbers and cell is trying to do.