## Sunday puzzle (multi steps)

Post puzzles for others to solve here.

### Re: Sunday puzzle (multi steps)

creint wrote:
If 7r4c1 is true then it leads to no 4 possible in c4, so it can be removed.
Starting at Blue point (false) and follow the manual added blue line.
Note that blue point was group 7r56c2 = 7r3c2 .., but gets reduced to a single in the end.
Note that 7r4c4 was already excluded at start of chain.
Note that . refers to 4r57c4
Another name could be something like "unit contradiction in net".

The graphic is good (though it doesn't display the continuity of the sequence of candidates), but there is no "group".
"." doesn't refer to anything but to the absence of a candidate that is neither t- nor z-. There's no need for any exotic name for it.
Last edited by denis_berthier on Mon Mar 01, 2021 5:48 am, edited 1 time in total.
denis_berthier
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### Re: Sunday puzzle (multi steps)

I try to translate whip(9) into graphical representation as follows :
whip(9).PNG (98.07 KiB) Viewed 123 times

7r56c2 = (7-2)r3c2 = (2-5)r2c2 = r8c2 - r8c4 = (5=7)r7c4 = r4c4|(r5c4 - ALS(7=81)r4c4r5c5 - (1=4)r1c5 - 4r2c4 =>Contradiction as No 4 in C4) => r4c1<>7
yzfwsf

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### Re: Sunday puzzle (multi steps)

yzfwsf wrote:I try to translate whip(9) into graphical representation as follows :
whip(9).PNG

7r56c2 = (7-2)r3c2 = (2-5)r2c2 = r8c2 - r8c4 = (5=7)r7c4 = r4c4|(r5c4 - ALS(7=81)r4c4r5c5 - (1=4)r1c5 - 4r2c4 =>Contradiction as No 4 in C4) => r4c1<>7

FAILED. See creint's graphic for a better starting point. creint has understood that the z- and t- candidates are not part of the whip.
denis_berthier
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### Re: Sunday puzzle (multi steps)

Hello,
jco wrote:(...)
1. (7)r9c13=(7)r9c5-(8)r9c5=(8)r9c1-(8=7)r4c1-(7=8)r4c4 => -7 r7c1, -8 r8c4, -8 r56c5
(...)
2. (5)r7c4=r8c4-(5=287)b7p457-(7)r4c1=(7)r4c4 => -7 r7c4; lclste
(...)

The elimination of (7) r7c1 is unnecessary (so no need for two SIS in one AIC), but if I follow Leren's idea and perform SS first, and modify slightly my previous second step:

1. SS (8)r9c5=r9c1-r4c1=(8)r4c4 => -8 r56c5, -8 r8c4

Code: Select all
`   1      2    3       4      5      6     7    8    9.-------------------+--------------------+---------------.|  3      9    8    |  2      14     5   | 7    14   6   | 1|  6      25   15   |  149    3      7   | 8    124  59  | 2|  4      257  157  |  19     6      8   | 159  123  359 | 3|-------------------+--------------------+---------------|| b78     3    4    | a78     5      9   | 2    6    1   | 4|  5     c178  6    |  1478   1247   124 | 3    9    78  | 5|  9     c178  2    |  3      17     6   | 4    5    78  | 6|-------------------+--------------------+---------------||  17     6    3579 | e145-7  1479   134 | 159  8    2   | 7|  128   c58   359  | d15     1289   123 | 6    7    4   | 8|  1278   4    579  |  6      12789  12  | 159  13   359 | 9'-------------------+--------------------+---------------'`

2. (7)r4c4=r4c1-(7=185)r568c2-(5)r8c4=(5)r7c4 => -7 r7c4; lclste
Regards,
jco

Edit: fixed writing to lclste
Last edited by jco on Wed Mar 03, 2021 12:02 pm, edited 2 times in total.
JCO
jco

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### Re: Sunday puzzle (multi steps)

Here is a graphical representation of the above whip[9]:

All the candidates that belong to the pattern are displayed in bold, either green or red.
The target is underlined.
Red means FALSE if the target is TRUE.
Green means TRUE if the target is TRUE.
Arrows indicate the sense of reading.
Thin lines: TRUE to FALSE.
Thick lines: FALSE to TRUE.
(Notice that TRUE and FALSE don't apply to the whip pattern itself, but to how it can be used for inferences.)

Candidates in a cell have been ordered in order to make it easier to draw lines.

You will notice that there is a single continuous line, going from the target to the end point (the final dot).
Last edited by denis_berthier on Wed Mar 03, 2021 5:41 am, edited 3 times in total.
denis_berthier
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### Re: Sunday puzzle (multi steps)

The above pdf converted to png:
Whip[9]-1.png (76.39 KiB) Viewed 98 times
urhegyi

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### Re: Sunday puzzle (multi steps)

denis_berthier wrote:
AnotherLife wrote:Now it is possible to get a one-step solution with a forcing net. [...]

Starting with the same PM, the same elimination was obtained by my last whip[9] instead of this complicated net.

Mon bon monsieur, now I see from urhegyi's picture that your logic is the same as in my forcing net. Have you seen my picture? https://disk.yandex.ru/i/rBJo3ttnB5sQeg I also see that you omitted some important links such as r4c1=7 => r5c2<>7, r3c2=7 => r3c2<>5, r4c1=7 => r4c4<>7, r5c4=7 => r6c5<>7. Without these links, you would not have had the corresponding strong links in your picture. Would you tell me why you consider my forcing net complicated as opposed to your whip[9]? It is virtually the same.
Bogdan
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### Re: Sunday puzzle (multi steps)

AnotherLife wrote:now I see from urhegyi's picture that your logic is the same as in my forcing net. Have you seen my picture? https://disk.yandex.ru/i/rBJo3ttnB5sQeg I also see that you omitted some important links such as r4c1=7 => r5c2<>7, r3c2=7 => r3c2<>5, r4c1=7 => r4c4<>7, r5c4=7 => r6c5<>7. Without these links, you would not have had the corresponding strong links in your picture. Would you tell me why you consider my forcing net complicated as opposed to your whip[9]? It is virtually the same.

If you consider a single continuous line is the same as 3 lines developing in parallel from a trivalue cell, there's no point talking more about it.
As for the z- and t- candidates and the "missing" links in my graphic, if you can't understand abstraction, there's also no point talking more about it.
denis_berthier
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### Re: Sunday puzzle (multi steps)

denis_berthier wrote:If you consider a single continuous line is the same as 3 lines developing in parallel from a trivalue cell, there's no point talking more about it.
As for the z- and t- candidates and the "missing" links in my graphic, if you can't understand abstraction, there's also no point talking more about it.

1. Where is this trivalue cell?
2. I have a diploma in mathematics of Moscow State University, and I am ok with abstraction.
3. I do not 'play' with sudokus but consider them as mathematical problems.

I would like other members of the forum to express their opinion about these solutions and their main difference, if any.
Bogdan
AnotherLife

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### Re: Sunday puzzle (multi steps)

AnotherLife wrote:
denis_berthier wrote:If you consider a single continuous line is the same as 3 lines developing in parallel from a trivalue cell, there's no point talking more about it.
As for the z- and t- candidates and the "missing" links in my graphic, if you can't understand abstraction, there's also no point talking more about it.

1. Where is this trivalue cell?
2. I have a diploma in mathematics of Moscow State University, and I am ok with abstraction.
3. I do not 'play' with sudokus but consider them as mathematical problems.
I would like other members of the forum to express their opinion about these solutions and their main difference, if any

As you're anonymous, you can claim all the diplomas you like. No one can check.
But no, you are not ok with abstraction if you don't understand that the z- and t- candidates (and the associated links) don't belong to the whip - by definition of a whip.
And you are not ok with maths in general if you don't understand that a single line and 3 (or more) lines are not the same thing.
denis_berthier
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### Re: Sunday puzzle (multi steps)

AnotherLife wrote:
denis_berthier wrote:As you're anonymous, you can claim all the diplomas you like. No one can check.

I am not used to a conversation in such a tone. I do not have to show any diplomas to conceited and ill-bred persons. No more discussion with you.

Great. This is a great excuse for not answering the technical points.
Anyway, that was bound to lead nowhere!
denis_berthier
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### Re: Sunday puzzle (multi steps)

denis_berthier wrote:
creint wrote:
If 7r4c1 is true then it leads to no 4 possible in c4, so it can be removed.
Starting at Blue point (false) and follow the manual added blue line.
Note that blue point was group 7r56c2 = 7r3c2 .., but gets reduced to a single in the end.
Note that 7r4c4 was already excluded at start of chain.
Note that . refers to 4r57c4
Another name could be something like "unit contradiction in net".

The graphic is good (though it doesn't display the continuity of the sequence of candidates), but there is no "group".
"." doesn't refer to anything but to the absence of a candidate that is neither t- nor z-. There's no need for any exotic name for it.

When you are reading the logic from left to right you don't see why 7r5c2 is not used.
I think most readers try to read step by step. A bit more details would improve the readability for most of readers, they probably don't have an user interface that can display the whips.
-For some readers it should include both candidates if they are both used in a Strong link: -7r56c2 -> 7r3c2, on its own -7r6c2 -> 7r3c2 is invalid (7r5c2 could also be true).
-For some readers include 7r4c1 -> -7r4c4, because it is an extra step the user has to do when manually drawing. It could be read as invalid because -7r7c4 -> 7r5c4 by itself is invalid (7r4c4 could also be true).

If 7r56c2 are both are excluded by rest of chain you would have given ".".
Why are other false points shown? With more abstraction you only need true points in the right order and you can construct the logic. For example: 7r4c1 - c2n7{r3} - c2n2{r2} - c2n5{r8}.

*Links on this forum do work but it probably should not contain [] characters.
creint

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### Re: Sunday puzzle (multi steps)

creint wrote:
denis_berthier wrote:
creint wrote:If 7r4c1 is true then it leads to no 4 possible in c4, so it can be removed.
Starting at Blue point (false) and follow the manual added blue line.
Note that blue point was group 7r56c2 = 7r3c2 .., but gets reduced to a single in the end.
Note that 7r4c4 was already excluded at start of chain.
Note that . refers to 4r57c4
Another name could be something like "unit contradiction in net".

The graphic is good (though it doesn't display the continuity of the sequence of candidates), but there is no "group".
"." doesn't refer to anything but to the absence of a candidate that is neither t- nor z-. There's no need for any exotic name for it.

When you are reading the logic from left to right you don't see why 7r5c2 is not used.
I think most readers try to read step by step. A bit more details would improve the readability for most of readers, they probably don't have an user interface that can display the whips.
-For some readers it should include both candidates if they are both used in a Strong link: -7r56c2 -> 7r3c2, on its own -7r6c2 -> 7r3c2 is invalid (7r5c2 could also be true).
-For some readers include 7r4c1 -> -7r4c4, because it is an extra step the user has to do when manually drawing. It could be read as invalid because -7r7c4 -> 7r5c4 by itself is invalid (7r4c4 could also be true).
If 7r56c2 are both are excluded by rest of chain you would have given ".".

In my graphic, the link between the target and the first llc is drawn.
For the rest, the fundamental point you're still missing is, a whip is NOT a chain of inferences. It is a static pattern, a continuous sequence of candidates, visible in a grid without any logic reasoning. The z- and t- candidates are irrelevant: they could disappear (by another rule being applied before this whip), the whip pattern would remain UNCHANGED.
The whip pattern can be USED as a support for inferences and only then does one need to take the z- and t-candidates into account MOMENTARILY, for a single step along the chain. For each of these candidates, it is straightforward to check that it is linked to the target or to a previous rlc. (Such volatile links could optionally be drawn in thin dotted lines, but certainly not in any way that would imply confusion with the real whip.)
I think the main problem for some people here is getting rid of the view of a chain as a chain of inferences. I have already talked about some unwanted consequences of this old view, such as the inability to understand that a chain is a pattern like any other pattern (Subset...) or such as counting the inference steps as a measure of complexity.

creint wrote:Why are other false points shown? With more abstraction you only need true points in the right order and you can construct the logic. For example: 7r4c1 - c2n7{r3} - c2n2{r2} - c2n5{r8}.

Absurd. This would hide one of the main properties of the chain, continuity.
This would not be more abstraction, but only destruction of the right level of abstraction. This is what Robert has done in his downgraded version of whips/braids/S-braids under the name of (anti-)tracks.

Beauty is in the eye of the beholder. Show Notre-Dame to some people, they will see a marvel of architecture. Show it to other people (AnotherName), they will only see tons of limestone that can be assembled in any way. Show it to still other people (Robert), they will want to eliminate the roof and install a pool on it instead.
What I'm asking is simple: respect my definitions; they are not arbitrary; every part of them has its reasons. If someone doesn't understand them or doesn't like them, it's not a problem for me: don't use them. But if someone hasn't even read the definitions, the only thing he may honestly do is keep his mouth shut.
(I'm not talking about you, creint; I think you understand them, in spite of some remaining confusion).

creint wrote:*Links on this forum do work but it probably should not contain [] characters.

I had used links before and I wondered why this didn't work. I have renamed it and it works. Thanks for the tip.
Also note that for including an image from the web, the tags should be [img] and not [url]. Using this would avoid having to follow links to unreliable sites.
denis_berthier
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### Re: Sunday puzzle (multi steps)

Image still won't load on my side (connection timeout):
https://denis-berthier.pagesperso-orange.fr/Misc/Whip9.pdf
Probably something with your site, don't know if pdfs can be loaded as in [img].

The link from urhegyi, does work but takes storage on this forum:

Posting to https://imgbb.com/ works for me.
creint

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### Re: Sunday puzzle (multi steps)

creint wrote:Image still won't load on my side (connection timeout):
https://denis-berthier.pagesperso-orange.fr/Misc/Whip9.pdf
Probably something with your site, don't know if pdfs can be loaded as in [img].

Could you try this https://denis-berthier.pagesperso-orange.fr
and also this https://denis-berthier.pagesperso-orange.fr/Misc/Whip9.png

to check what's wrong with my links?

I also try with the [img] tag
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