The New Sudoku Players' Forum

[eleven]

Maybe we should say clearer, what we understand as "manually" solving.
By "manually" i mean just using a simple program, which fills in the candidates, and shows singles and subsets, and thus helps to make the cumbersome work to evaluate, which of the found steps are not necessary. I think i am in line with totuan here.
Some years ago i took the time to solve a long puzzle (harder than this one) this way, and it turned out, that my solution was very similar to Robert's. So i assume, that he solves them manually (in this sense), too.
His steps (at least there and here) can be written as AIC's with minor extensions, so i find them nearer to AIC's than whips, braids & co.

[denis_berthier]

1) It should nevertheless be pointed out that Robert does not work only with paper and pencil.
He obviously has graphic tools and he can notably know if a track from any candidate leads to a contradiction (using singles and perhaps more) by clicking on a button.
It's not a secret, everyone can check it by going to assistant-sudoku.com

OK. But calling it manual solving when a single button applies a full T&E procedure is a blatant lie.
It reminds me of someone who claimed to solve his puzzles manually because poor him entered the givens into a solver with his own little fingers.

2) So I would like to know what you think of P.O.’s chains....

OOT. Ask in another thread.

3) Truly, I don't think this algorithm "Fewer-Steps" is some “confidential defense”, you yourself made a thread about it: [Advanced solving techniques] – [Reducing the number of steps].

Note that I said (and wrote both in PBCS and the BUM) that it was due to you. I didn't surreptitiously introduce the algorithm in SudoRules without saying it or with saying that I had found it "on my own" without knowing what you were doing.
What I said is, one cannot use this algorithm manually. Robert is claiming to solve his puzzles manually. This is computationally impossible for the fewer steps part and you just confirmed it was also false for the TDP part.

[Mauriès Robert]

As eleven says, we need to be clear about what we mean by manual resolution, and his definition is indeed mine. Solving by hand does not exclude that we have to make several attempts at marking before finding the right one, but we do it by hand, with a pencil on paper, or on a computer graphics application. But in no case do we use a solver to help us.
But contrary to what Denis thinks, who calls me a liar (which is unacceptable), I do not use the button François talks about to solve, nor do I use a solver because I have one.
My way of solving, which is the basis of TDP, consists in using pairs of candidates (or pairs of sets of candidates) of which at least one allows a significant development of a track (or anti-track), without doing T&E, but by looking for interactions between the two tracks. This requires observation, practice and, of course, unsuccessful attempts.
The advantage of a graphic application like mine over paper/pencil is that colour marking and "eraser" are more practical and efficient.

Thank you eleven for noting that what I do is closer to the AIC technique than to Denis', which I agree with
Robert

[denis_berthier]

Solving by hand does not exclude that we have to make several attempts at marking before finding the right one, but we do it by hand, with a pencil on paper, or on a computer graphics application. But in no case do we use a solver to help us.

Having the "graphics application" do the markings and the erasing (i.e. the T&E procedure) can't be considered as manual solving.

My way of solving, which is the basis of TDP, consists in using pairs of candidates (or pairs of sets of candidates) of which at least one allows a significant development of a track (or anti-track), without doing T&E, but by looking for interactions between the two tracks.

False. This is what you called conjugated tracks (equivalent to Forcing T&E) but this is not what appears now in your resolution paths.

Thank you eleven for noting that what I do is closer to the AIC technique than to Denis', which I agree with

Your tracks have nothing to do with AICs. AICs are reversible, your tracks are not. Eleven cannot ignore this.

[eleven]

Would you point to a non reversible step please ?

[denis_berthier]

Would you point to a non reversible step please ?

Tracks in general are not reversible; fullstop.
For a track in particular, nobody can tell without reconstructing the missing information (llcs and csps). I'm not gonna waste my time doing this whenever Robert publishes his things.

You claimed that Robert's solution was AICs; it's your job to write it as AICS to prove your claim. Good luck.

[Mauriès Robert]

Solving by hand does not exclude that we have to make several attempts at marking before finding the right one, but we do it by hand, with a pencil on paper, or on a computer graphics application. But in no case do we use a solver to help us.

Having the "graphics application" do the markings and the erasing (i.e. the T&E procedure) can't be considered as manual solving.

The graphics application I use does nothing for me in terms of choosing which candidates to mark, it just puts a colour on the candidate when I click with the mouse on that candidate. So I maintain that it is manual because there is no assistance in the decision.

My way of solving, which is the basis of TDP, consists in using pairs of candidates (or pairs of sets of candidates) of which at least one allows a significant development of a track (or anti-track), without doing T&E, but by looking for interactions between the two tracks.

False. This is what you called conjugated tracks (equivalent to Forcing T&E) but this is not what appears now in your resolution paths.

This proves once again that you do not try to understand what I do, preferring to criticise in order to denigrate. So I explain to you what I have already largely explained elsewhere:
The conjugate track P associated with an anti-track P' obtained by deleting A is the track obtained by validating A. P contains A and in this case the pair of sets used is formed by A and the set of other candidates in A's cell. By developing only the anti-track P' and then eliminating a candidate that sees A and a candidate from P', I am only exploiting an interaction of the two conjugate tracks P and P'. So no contradiction with what I have always done.

Thank you eleven for noting that what I do is closer to the AIC technique than to Denis', which I agree with

Your tracks have nothing to do with AICs. AICs are reversible, your tracks are not. Eleven cannot ignore this.

Read again what eleven wrote to contradict your comments suggesting that anti-tracking is inspired by what you do with your whips and braids, and that my resolutions are not manual. In particular, he doesn't say that the tracks are AIC's. It says that:
His steps (at least there and here) can be written as AIC's with minor extensions, so i find them nearer to AIC's than whips, braids & co..

Robert

[denis_berthier]

Solving by hand does not exclude that we have to make several attempts at marking before finding the right one, but we do it by hand, with a pencil on paper, or on a computer graphics application. But in no case do we use a solver to help us.

Having the "graphics application" do the markings and the erasing (i.e. the T&E procedure) can't be considered as manual solving.

The graphics application I use does nothing for me in terms of choosing which candidates to mark, it just puts a colour on the candidate when I click with the mouse on that candidate. So I maintain that it is manual because there is no assistance in the decision.

This is not what François says. According to him, it tells whether the candidate can be eliminated (in essence by T&E) or not. Unfortunately, I can't try it by myself as it seems your website requires a code.

Thank you eleven for noting that what I do is closer to the AIC technique than to Denis', which I agree with

Your tracks have nothing to do with AICs. AICs are reversible, your tracks are not. Eleven cannot ignore this.

Read again what eleven wrote ..l. In particular, he doesn't say that the tracks are AIC's. It says that:
His steps (at least there and here) can be written as AIC's with minor extensions, so i find them nearer to AIC's than whips, braids & co..

I can trust eleven for systematically opposing what I say. What's the value of such a guy's opinion, especially when it's supported by no evidence?
If you consider yourself that your tracks are close to AICs, you've obviously understood nothing of AICs. A track is a set of candidates (an AIC is a sequence), a track doesn't require continuity, a track is generally not reversible...

I'm still waiting eleven's re-writing of your tracks as "near" AICs.
What are the "minor extensions"? z- and t-candidates?
And what does the restriction "here and there" mean? Of course some tracks, same as some braids, can be written as e.g. bivalue chains, because they are very special cases. So, the whole sentence with this restriction doesn't mean anything.

[Mauriès Robert]

This is not what François says. According to him, it tells whether the candidate can be eliminated (in essence by T&E) or not. Unfortunately, I can't try it by myself as it seems your website requires a code.

You have misunderstood what François means. My website has a button, accessible to all without needing a code, that allows you to mark all the candidates of a track at once rather than doing it candidate by candidate. It is a facility offered to avoid wasting time in this marking, but no one is obliged to use it, in the same way that one can use the puzzle with all the candidates positioned or not, as proposed by all the sudoku websites.
This button does not indicate if the track is invalid except in the case where the marking leads to a contradiction as it would be seen by marking candidate after candidate.
This being said, I have access like everybody else to various websites or softwares (not yours) which propose aided solving, but when I say that I have done a manual solving, it is because I have not used these softwares, you cannot question my intellectual honesty.

I can trust eleven for systematically opposing what I say. What's the value of such a guy's opinion, especially when it's supported by no evidence?
If you consider yourself that your tracks are close to AICs, you've obviously understood nothing of AICs. A track is a set of candidates (an AIC is a sequence), a track doesn't require continuity, a track is generally not reversible...

I'm still waiting eleven's re-writing of your tracks as "near" AICs.
What are the "minor extensions"? z- and t-candidates?
And what does the restriction "here and there" mean? Of course some tracks, same as some braids, can be written as e.g. bivalue chains, because they are very special cases. So, the whole sentence with this restriction doesn't mean anything.

I don't dispute the fact that a runway is not an AIC and that it is not reversible in general, we've talked about that in the past.
I understand eleven's intervention only as a proof that my anti-tracks which are identical, in simple cases, to AICs are not vague copies of your braids whatever you say, but a different approach conceived independently of the other concepts and which leads to identical results.

[denis_berthier]

This is not what François says. According to him, it tells whether the candidate can be eliminated (in essence by T&E) or not. Unfortunately, I can't try it by myself as it seems your website requires a code.

You have misunderstood what François means. My website has a button, accessible to all without needing a code, that allows you to mark all the candidates of a track at once rather than doing it candidate by candidate. It is a facility offered to avoid wasting time in this marking, but no one is obliged to use it, in the same way that one can use the puzzle with all the candidates positioned or not, as proposed by all the sudoku websites. This button does not indicate if the track is invalid except in the case where the marking leads to a contradiction as it would be seen by marking candidate after candidate

Those are totally different functionalities. Positioning the candidates is doing paperwork. Marking all the candidates depending on another one C being true or false as true or false until an error is possibly reached is doing a full T&E run for C.

This being said, I have access like everybody else to various websites or softwares (not yours)

CSP-Rules has been public since July 2021 and it runs on any operating system. You have access to it. You may not want to use it, that's a different matter, but you do have access to it.
Strange that you feel the need to claim the contrary, when anybody can check you're wrong.

I can trust eleven for systematically opposing what I say. What's the value of such a guy's opinion, especially when it's supported by no evidence?
If you consider yourself that your tracks are close to AICs, you've obviously understood nothing of AICs. A track is a set of candidates (an AIC is a sequence), a track doesn't require continuity, a track is generally not reversible...

I'm still waiting eleven's re-writing of your tracks as "near" AICs.
What are the "minor extensions"? z- and t-candidates?
And what does the restriction "here and there" mean? Of course some tracks, same as some braids, can be written as e.g. bivalue chains, because they are very special cases. So, the whole sentence with this restriction doesn't mean anything.

I don't dispute the fact that a runway is not an AIC and that it is not reversible in general, we've talked about that in the past.
I understand eleven's intervention only as a proof that my anti-tracks which are identical, in simple cases, to AICs are not vague copies of your braids whatever you say, but a different approach conceived independently of the other concepts and which leads to identical results.

Logical fallacy.
Braids are also identical to AICs in simple cases.

[eleven]

Would you point to a non reversible step please ?

Tracks in general are not reversible; fullstop.
For a track in particular, nobody can tell without reconstructing the missing information (llcs and csps). I'm not gonna waste my time doing this whenever Robert publishes his things.

You claimed that Robert's solution was AICs; it's your job to write it as AICS to prove your claim. Good luck.

I can trust eleven for systematically opposing what I say. What's the value of such a guy's opinion, especially when it's supported by no evidence?
If you consider yourself that your tracks are close to AICs, you've obviously understood nothing of AICs. A track is a set of candidates (an AIC is a sequence), a track doesn't require continuity, a track is generally not reversible...

I'm still waiting eleven's re-writing of your tracks as "near" AICs.
What are the "minor extensions"? z- and t-candidates?
And what does the restriction "here and there" mean? Of course some tracks, same as some braids, can be written as e.g. bivalue chains, because they are very special cases. So, the whole sentence with this restriction doesn't mean anything.

Ok, so you prefer just to claim something than to read, what you are criticizing. I guess, you remembered, that Robert's chains are not reversible, which certainly is correct for some, but it is also correct for some chains, which are written in AIC notation.
In those both Robert and the AIC writers mark this explicitely, another common point, and different to your chains, which in my eyes makes them both harder to find and to read for humans.
Let's have a look at Robert's first chain, one of the most complex here.
This is, how i would write it in (extended) AIC notaion:

Code: Select all

+----------------------+----------------------+-----------------------+
| 4      2      6      |d1358   158    18     |ca13     9      7      |
|c13     7      5      |d139    2      169    |  8     b136    4      |
| 9      18    f38     |e134    7      146    | a136    5      2      |
+----------------------+----------------------+-----------------------+
| 1256   3      289    | 189    189    7      |  4      1268   15689  |
| 167    1689  g789    | 2      4      5      | h1369   1368   1689   |
| 125    1589   4      | 6      189    3      | i129    7      1589   |
+----------------------+----------------------+-----------------------+
| 8      59    f279    |e14579  6      1249   | i129    12     3      |
|f267    69     1      |e789    3      289    |  5      4      689    |
| 2356   4      239    | 1589   1589   1289   |  7      1268   1689   |
+----------------------+----------------------+-----------------------+

1r13c7 = 1r2c8 - (1=3)r1c7,r2c1 - 3r12c4 = 347r378 - [(7r8c1 = r7c3) & (3=8)r3c3] - (7|8=9)r5c3 - r5c7 = 29r67c7 => -1r67c7
The point is, that the single steps are independent, while in your chains you have to search, which of the earlier steps justify it.
And there is no missing information here.
You know, that i am not an advocat for AIC. But it should be clear now, that Robert's method is nearer to them than to yours. So i think, there is absolutely no reason to claim, that he copied something from your work - apart from slating a competitor and having joy in unfriendly discussions.
btw you know, that there are many things you are saying, which i definitely agree with.

[denis_berthier]

I guess, you remembered, that Robert's chains are not reversible, which certainly is correct for some,

I was the 1st to have a look at Robert's tracks and the 1st to say that most (not "some") of them are not reversible.
[Indeed, this is not true of his tracks strictly speaking, because a track is defined as the set of candidates made true by a T&E procedure, not as a sequence. What Robert gives in his resolution paths are not even tracks but some linearisation or net-isation of them.
But let's pass over this; it's only due to Robert ignoring the difference between a set and a sequence.]

but it is also correct for some chains, which are written in AIC notation.

NO. The trademark of AICs has always been reversibility.
If you have non reversibility, either you have t- candidates, or you have branching. In no case can this be considered as belonging to the standard definition of AICs. You need extend the definitions upto the point where "AIC" means any chain/net, i.e. anything , i.e. nothing.

I will not comment your "AIC", because it's not an AIC: commas and "&" don't pertain to AIC notation.

The point is, that the single steps are independent, while in your chains you have to search, which of the earlier steps justify it.
And there is no missing information here.

It is false that the single steps of a track are independent in general. Like any T&E procedure, positive inferences rely on any previous negative ones.
The sequences of llcs and csps are definitely missing in tracks, as only positive inferences are written.
BTW, I don't have to search anything in my chains. z- and t- candidates can be verified step by step (by merely checking the presence of some fixed link) and need not be remembered for the next steps. How many times do I need to repeat this?

You know, that i am not an advocat for AIC. But it should be clear now, that Robert's method is nearer to them than to yours.

No. What's clear is to me is, either you are considering only very special cases of tracks or you are adopting a definition of AICs that is so generalised that it means nothing.

btw, that there are many things you are saying, which i definitely agree with.

Really? Can you point to a single recent place in this forum that would make this apparent? At some point in time, you turned against me for reasons I don't know and you've become systematically negative.

[eleven]

The point is, that the single steps are independent, while in your chains you have to search, which of the earlier steps justify it.
And there is no missing information here.

...
BTW, I don't have to search anything in my chains. z- and t- candidates can be verified step by step (by merely checking the presence of some fixed link) and need not be remembered for the next steps. How many times do I need to repeat this?

Well, i am not a beginner, but when i read your chains, i often wonder, where a link comes from. E.g. a recent chain by you here? If you applied the hidden pair 23 in box 9, the grid should be

Code: Select all

+-------------------+-------------------+-------------------+
| 2     179   39    | 3569  8     359   | 16    167   4     |
| 47    5     489   | 469   1     249   | 268   3     278   |
| 134   18    6     | 34    7     234   | 5     9     128   |
+-------------------+-------------------+-------------------+
| 356   268   2358  | 1     49    7     | 348   45    389   |
| 9     4     1     | 58    3     58    | 7     2     6     |
| 357   78    358   | 2     49    6     | 1348  145   1389  |
+-------------------+-------------------+-------------------+
| 146   126   7     | 348   5     1348  | 9     146   23    |
| 1456  3     459   | 479   2     149   | 146   8     17    |
| 8     129   249   | 3479  6     1349  | 23    147   5     |
+-------------------+-------------------+-------------------+

whip[7]: r1n7{c2 c8} - r1n1{c8 c7} - b3n6{r1c7 r2c7} - r8c7{n6 n4} - r9c8{n4 n1} - r9c2{n1 n2} - c7n2{r9 .} ==> r1c2≠9
Now i look at the link r9c8{n4 n1} - r9c2{n1 n2}. Why not 9 ? I have to look back to earlier steps to verify it. i don't mind, and even don't know, what exactly you mean with z- and t-candidates, fact is, i cannot find them in the chain. So how can i know them, when they are needed in a later step, without remembering (all of) them ?
Of course i can take a solver, and enter each step, let the solver do the simple eliminations and i will find it. But why should i not do some obviously more effective non-sequential moves then. Wouldn't it be stupid ?
I never saw such a thing in Robert's chains, without a mark, which earlier step allows this.
I don't say, that there is anything wrong with your chains, but as you know, i find them impracticable for manual solvers, and obviously they are not made for them.

[yzfwsf]

My understanding is:
t-candidates may be the meaning of target candidates, as the starting point in the chain. And z-candidates should be the candidates (rlc) contained in all preceding nodes of the chain.
I think whip is actually a reduced version of dynamic CRCD (cell / region / convention / double forcing chain), and dynamic CRCD is basically equivalent to braid.
However, the LLC formed by the RLC in braid and whip is mostly hidden.

[denis_berthier]

If you applied the hidden pair 23 in box 9, the grid should be

Code: Select all

+-------------------+-------------------+-------------------+
| 2     179   39    | 3569  8     359   | 16    167   4     |
| 47    5     489   | 469   1     249   | 268   3     278   |
| 134   18    6     | 34    7     234   | 5     9     128   |
+-------------------+-------------------+-------------------+
| 356   268   2358  | 1     49    7     | 348   45    389   |
| 9     4     1     | 58    3     58    | 7     2     6     |
| 357   78    358   | 2     49    6     | 1348  145   1389  |
+-------------------+-------------------+-------------------+
| 146   126   7     | 348   5     1348  | 9     146   23    |
| 1456  3     459   | 479   2     149   | 146   8     17    |
| 8     129   249   | 3479  6     1349  | 23    147   5     |
+-------------------+-------------------+-------------------+

I don't apply the hidden pair because this is not a simplest-first solution, but a fewer steps solution.
The resolution state is

Code: Select all

   +----------------+----------------+----------------+
   ! 2    179  39   ! 3569 8    359  ! 16   167 4    !
   ! 47   5    489  ! 469  1    249  ! 268  3    278  !
   ! 134  18   6    ! 349  7    234  ! 5    9    128  !
   +----------------+----------------+----------------+
   ! 356  268  2358 ! 1    49   7    ! 348  45   389  !
   ! 9    4    1    ! 58   3    58   ! 7    2    6    !
   ! 357  78   358  ! 2    49   6    ! 1348 145  1389 !
   +----------------+----------------+----------------+
   ! 146  126  7    ! 348  5    1348 ! 9    146  123  !
   ! 1456 3    459  ! 479  2    149  ! 146  8    17   !
   ! 8    129  249  ! 3479 6    1349 ! 1234 147  5    !
   +----------------+----------------+----------------+

and the chosen whip (maybe not the simplest pattern available but the one with the best score) is:
whip[7]: r1n7{c2 c8} - r1n1{c8 c7} - b3n6{r1c7 r2c7} - r8c7{n6 n4} - r9c8{n4 n1} - r9c2{n1 n2} - c7n2{r9 .} ==> r1c2≠9

Now i look at the link r9c8{n4 n1} - r9c2{n1 n2}. Why not 9 ?

9 where? A link is a link. There's no 9 in it.
If you mean why not 9 in r9c2{n1 n2}, it's obvious: because n9r9c2 is a z-candidate (linked to the target n9r1c2.

i don't mind, and even don't know, what exactly you mean with z- and t-candidates,

rofl. If you don't know what whips are, why are you talking so much about them, as if you knew.

fact is, i cannot find them in the chain. So how can i know them, when they are needed in a later step, without remembering (all of) them ?

You can't find z- or t- candidates in the whip/braid... descriptions because they are not part of these chain patterns, by definition. Fullstop.
If you don't understand this, you have a problem with abstraction and mathematical definitions. A mathematical definition must be taken as is, like it or not. It has to be judged by the results it allows.

When you want to check that the pattern stated in a resolution path is effectively a whip in the current resolution state, of course you need to check that the z- and t- candidates present in this state are linked to the target, resp. to a previous rlc. But you never need to remember z- or t- candidates for later use. I don't know why you keep repeating this bullshit that I have debunked many times.
Of course, what you need to remember is the chain itself, like any AIC. How do you build a full chain without remembering it?

I never saw such a thing in Robert's chains, without a mark, which earlier step allows this.

Now you have to explain how something that contains less information can be easier to understand. Tracks miss essential information about left-linking candidates and csp-variables, and they don't show the z- and t- candidates either. In addition to the z- and t- candidates that are directly observable in the resolution state, you have to guess the csp-vars and the llcs.

I don't say, that there is anything wrong with your chains, but as you know, i find them impracticable for manual solvers, and obviously they are not made for them.

Once more, the manual solver argument, the argument of people with no real argument. You keep repeating this bullshit. Whips are designed for manual solvers from the very beginning. They can replace myriad abstruse patterns. My readers and users of CSP-Rules use them daily. They need only short ones. Real world players don't solve 9.0 puzzles where long chains may be needed.
What you can say is, you don't like them, you are not trained to use them. I acknowledge you wrote "I find...". At least you understand that you're expressing only a personal opinion - biased against me, as usual.