Supersymmetries and Hidden chains

Advanced methods and approaches for solving Sudoku puzzles

Postby ravel » Tue Jul 24, 2007 2:16 pm

Denis,

please calm down. When you reread our posts, you will see, that neither re'born nor i was offending you.

re'born has asked you to explain, what you mean with "xyt-chains and xyzt-chains cannot be reduced to any known resolution rule".

You did not, but offended him.

What i said was:
"xyt-chains and xyzt-chains cannot be reduced to any known resolution rule" easily can be misinterpreted - not that it was wrong.

Now you explained, what you meant with it. Thats all we wanted and as far as i am concerned, i dont have more comments on this formulation.
So xyt-chains cannot be "reduced" to Nice Loops in this sense, ok. But i insist on that they can be written as nice loops. Since Carcul has written hundreds of nice loops, that contain more esprit than a xyt-chain, i really dont care, if one was under them.

Be sure that i dont want to mislead anybody. If i did, i did it without intention and want to apologize for that.
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Postby denis_berthier » Tue Jul 24, 2007 3:58 pm

ravel, re'born, I didn't feel offended (but rather disapointed, in comparison with the interesting discussions I had on the UK forum) and I had no intention to offense anyone.
What I'd like is we use rational arguments and not statements with no justifications.
"Insisting on that xyt-chains can be written as Nice Loops" is not really the kind of rational argument I am thinking of. Why don't you explain to us how you proceed to re-write them in this form?
(Don't spend too much time on this: you can't).
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Postby ravel » Tue Jul 24, 2007 7:41 pm

A suggestion:
Why dont you just post a puzzle from your book in the Help forum and look, what the members here do with it ?

[Added:]
Why don't you explain to us how you proceed to re-write them in this form?
Sorry, i needed a second look at this question to guess, what you want. My formulation was indeed very sloppy. So to say it more precisely:
Each concrete elimination, that is possible by means of xy(z)t-chains, can also be done with a nice loop. That means, that all puzzles, that can be solved with those chains (and a set of other techniques), can also be solved with nice loops (and the same set of other techniques).
I hope to have clarified that now.
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Postby denis_berthier » Wed Jul 25, 2007 7:40 am

ravel wrote:My formulation was indeed very sloppy. So to say it more precisely:
Each concrete elimination, that is possible by means of xy(z)t-chains, can also be done with a nice loop. That means, that all puzzles, that can be solved with those chains (and a set of other techniques), can also be solved with nice loops (and the same set of other techniques).
I hope to have clarified that now.


This is (and already was) clear, but this is precisely the kind of unsupported (and indeed false) claim that does not bring anything to the discussion, except expressing your personal wishes.

BTW, I've opened a thread for xyt-chains, the present one being dedicated to hidden chains.
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Postby ravel » Wed Jul 25, 2007 8:29 am

denis_berthier wrote:This is (and already was) clear, but this is precisely the kind of unsupported (and indeed false) claim that does not bring anything to the discussion, except expressing your personal wishes.
Please explain. Do you have an example of an elimination, that could not be expressed with a nice loop also ?
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Postby denis_berthier » Wed Jul 25, 2007 8:35 am

ravel wrote:Do you have an example of an elimination, that could not be expressed with a nice loop also ?

As I said, xyt-chains are discussed in the thread for xyt-chains.
Look at the example there and, for a start, try to express it as a Nice Loop.
And please answer in the other thread.
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Postby ronk » Fri Jul 27, 2007 10:26 am

udosuk wrote:And it wouldn't be too complicated to say perform a reverse translation from say a rn-table to the other 2 tables on another sheet. That way you can copy & paste data back and forth between sheets and there's no need to "mentally translate" any move.:idea:

I understand you mean like this ...
Code: Select all
Sheet 1. To paste, highlight and edit in rc-space

      rc --> rn
      |
      v
      cn


Sheet 2. To paste, highlight and edit in rn-space

      rc <-- rn
             /
           /
         v
      cn


Sheet 3. To paste, highlight and edit in cn-space

      rc     rn
      ^      ^
      |    /
      |  /
      cn

... where the arrows indicate automatic translation (computation) of pencilmarks into alternate spaces. Then one can copy computed pencilmarks from any one of two sheets to the appropriate third sheet to continue, and the translation formulas can be write-protected.

Since I'm not proficient enough in Excel to get "the same" with three pencilmark grids on one sheet, I guess that will have to do.:)
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Postby denis_berthier » Fri Jul 27, 2007 10:55 am

ronk, udosuk, I'm not an expert in Excel, but copying in three directions seems overly complex.
rc-space remains the main grid, rn- and cn- are (very helpful) auxiliaries.
One can admit that you do any elimination in rc-space (i.e. when the pattern of a rule is detected in rn- or cn- space, its conclusions can be applied directly in rc-space instead of rn- or cn-). This is not error prone if you consider that you have to eliminate RiCjNk, in whatever space you do it.
This is justified because what is difficult is spotting the patterns, not applying the conclusions of a rule.
This way, rn- and cn- spaces can be maintained automatically (and can be write protected).
udosuk, as I understand it, this how the the tool you have developed works. If you could make it available, I think it would be helpul to all those who'd like to try the extended board before they decide to invest time building it by hand when they have no computer with them.
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Postby re'born » Fri Jul 27, 2007 11:08 am

Denis,

I've just finished working through my own proofs of what you claim in the opening thread of this post (and of course your book) and your conclusions are both correct (not that you were in doubt) and very satisfying. When I first read Arcilla's idea to write down these companion grids (i.e., your rn and cn spaces) I only thought of them in terms of one candidate. Arcilla pointed out how they could be used to find basic fish and I saw quite easily how to extend them to finned fish (as well as sashimi, but I agree with ronk that the distinction is somewhat pointless). It wasn't clear how to extend the results to franken fish and mutant fish and that it probably because of block considerations. I eventually tried to look at the entire rn (resp. cn) space and see what could be done, but aside from noticing that a naked pair in a column corresponded to a hidden pair in rc-space, I couldn't make any reasonable conclusions. Since I'm pretty good at finding hidden pairs without going first to rn-space, I discarded the idea. I am glad to see that you succeeded where I failed.

I started playing around with these things and I saw a very nice example. Unfortunately the puzzle is lost (I have a 2-year old who doesn't understand what happens when you combine paper with liquids), but I do have the diagram of the exclusion. I thought I might share it since this thread seems to not have too many examples yet.

The original grid contained something similar to this
Code: Select all
   .   . 1458|   .   .   . |   .   .   .
   .   . 2458|   .   .   . |  128  .   .
   .   .   57|   .   .   . |   35  .   .
 ------------+-------------+------------
   .   .   . |   .   .   . |   .   .   .
   .   .   . |   .   .   . |   .   .   .
   .   .   . |   .   .   . |  589  .   .
 ------------+-------------+------------
   .   .   . |   .   .  .  |   .   .   .
   .   .   . |   .   .  .  |   .   .   .
   .   .   . |   .   .  .  |   .   .   .

with accompanying (partial) cn-space (hopefully I am staying consistent with Denis' orientation)
Code: Select all
   .   .   . |   .   .   . |   .   .   .
   .   .   . |   .   .   . |   .   .   .
   .   .   . |   .   .   . |   .   .   .
 ------------+-------------+------------
   .   .  12 |   .   .   . |   .   .   .
   .   . 123 |   .   .   . |   36  .   .
   .   .   . |   .   .   . |   .   .   .
 ------------+-------------+------------
   .   .   . |   .   .   . |   .   .   .
   .   .   . |   .   .   . |   26  .   .
   .   .   . |   .   .   . |   .   .   .

By viewing this as an almost xy-chain (or using the ALS xz-rule) we see that in the cn-space, r8c3<>2, which in rc-space translates to r2c3<>8. I doubt I ever would have found this deduction (remembering that I was not looking at just the partial grid above) without first translating to cn-space.

To me, the utility of this technique is clear. Hopefully, the next generation of solvers will build these in as it would make the process of finding some killer eliminations much easier.
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Postby ronk » Fri Jul 27, 2007 1:18 pm

denis_berthier wrote:I'm not an expert in Excel, but copying in three directions seems overly complex.

Mimicking someone somewhere ... I don't recall writing that one must use sheets 2 and 3, fullstop.
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Postby denis_berthier » Fri Jul 27, 2007 2:48 pm

re'born wrote:Denis,
I've just finished working through my own proofs of what you claim in the opening thread of this post (and of course your book) and your conclusions are both correct (not that you were in doubt) and very satisfying.
(…)
To me, the utility of this technique is clear. Hopefully, the next generation of solvers will build these in as it would make the process of finding some killer eliminations much easier.

re'born, thanks for this. I wish we soon have a tool for automatically generating the rn- and cn- representations.

re'born wrote:this thread seems to not have too many examples yet.

Nobody asked. Here are a few more (still easy ones) with their solution. As you have seen in the book, there are many more complex ones. In my web pages (online supplements section, you can find lots of puzzles, organised by the level at which SudoRules classifies them (i.e. the length of the longest chain necessary to solve them - just a pragmatic measure of complexity).

2968.37.5
78456.2.3
1357.2..6
4231765..
.513.4672
67.25.431
5679..324
31.425.67
.4263715.
***** SudoRules version 12 *****
row R3 : hxy5-cn-chain on cn-cells C5N9*, C5N8, C6N8, C3N8 and C7N8* with rows R3, R5, R7, R6 and R8
==> R3 eliminated from the cn-candidates for C7N9
i.e. 9 eliminated from the candidates for R3C7
… (Naked-Singles and Hidden-Singles)
296813745
784569213
135742896
423176589
851394672
679258431
567981324
318425967
942637158


.8.2.1…
14.385.92
.2.9.4.18
.3.758261
261493.8.
8..612934
.98137.2.
…8291.3
312546879
***** SudoRules version 12 *****
number 6 : row R8 interaction with block B7
==> 6 eliminated from the candidates for R7C1
column C7 : hxy5-rn-chain on rn-cells R1N3*, R1N9, R4N9, R4N4 and R7N4* with columns C7, C3, C1, C3 and C1
==> C7 eliminated from the rn-candidates for R1N4
i.e. 4 eliminated from the candidates for R1C7
… (Naked-Singles and Hidden-Singles)
983271645
146385792
725964318
439758261
261493587
857612934
598137426
674829153
312546879
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Postby udosuk » Fri Jul 27, 2007 3:56 pm

ronk wrote:
denis_berthier wrote:I'm not an expert in Excel, but copying in three directions seems overly complex.

Mimicking someone somewhere ... I don't recall writing that one must use sheets 2 and 3, fullstop.

You guys misunderstood me. No need for any multi-sheet inferences. In fact you can do it on one single sheet, but using 2 sheets is perhaps a bit more tidy.

On the main sheet (or area) you have a 9x9 rc-space grid, and 2 resulting 9x9 grids using formulas to produce the rn- & cn-spaces.

On the 2nd sheet (or area) you have a 9x9 rn-space grid, where you can do the editing, and a resulting 9x9 grid using formulas to produce the correspondent rc-space grid.

Below that you have another 9x9 area for a cn-space grid, where you can do the editing, and a resulting 9x9 grid using formulas to produce the correspondent rc-space grid.

So the operation is like this. From the main sheet (area) you can see all 3 grids. If you spot moves from the rc-space, fine, just edit on it directly, and the rn- & cn-space grids will change automatically.

If you spot moves from the rn- or cn-spaces, don't edit on them directly. Instead, copy & paste them to Notepad first, then immediately copy & paste the whole data from Notepad back to the secondary sheet (area) on the corresponding rn- or cn-space. There you can do the editing and the resulting rc-space will be updated automatically.

After you finish the move you can use the same method to copy & paste the updated rc-space back to the main sheet (area), in that case you will easily obtain the current state of all 3 grids without any mental translation of the moves.

To make life easier I always have a blank Notepad window open. Also keep using [alt-tab] to switch between windows instead of rolling that annoying mouse.

Hope I've made myself clearer this time.:idea:
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Postby denis_berthier » Fri Jul 27, 2007 4:24 pm

udosuk, I only meant that all the eliminations done by the player can be done in the main rc-grid - which doesn't seem much harder than copying and changing sheets.
Your tool allows both styles of use. Did you try the one I'm suggesting?
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Postby re'born » Fri Jul 27, 2007 4:57 pm

denis_berthier wrote:.8.2.1…
14.385.92
.2.9.4.18
.3.758261
261493.8.
8..612934
.98137.2.
…8291.3
312546879

In this puzzle, you've inadvertantly replaced "."'s with elipses in row 1 and row 8. This makes it rather troublesome to copy into solvers.
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Postby denis_berthier » Fri Jul 27, 2007 5:20 pm

re'born wrote:
denis_berthier wrote:.8.2.1…
14.385.92
.2.9.4.18
.3.758261
261493.8.
8..612934
.98137.2.
…8291.3
312546879

In this puzzle, you've inadvertantly replaced "."'s with elipses in row 1 and row 8. This makes it rather troublesome to copy into solvers.

re'born, thanks for signaling it. In my navigator, I don't see that. Have you corrected it in the above?
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