The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|..1|8..|
 |...|...|.2.|
 |9..|38.|47.|
 |---+---+---|
 |...|2..|13.|
 |3..|9.6|..2|
 |.56|..3|...|
 |---+---+---|
 |.27|.45|..3|
 |.9.|...|...|
 |..3|6..|...|
 *-----------*


Play/Print this puzzle online

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 |a47    3     2     |b47    9     1     | 8     6     5     |
 | 1478  1478  148   | 5     6    c47    | 3     2     9     |
 | 9     6     5     | 3     8     2     | 4     7     1     |
 *-------------------+-------------------+-------------------|
 | 7-48  478   9     | 2     5    d48    | 1     3     6     |
 | 3     148   148   | 9     7     6     | 5     48    2     |
 | 2     5     6     | 48    1     3     | 9     48    7     |
 *-------------------+-------------------+-------------------|
 |g18    2     7     |f18    4     5     | 6     9     3     |
 | 6     9     148   | 178   3    e78    | 2     5     48    |
 | 5     48    3     | 6     2     9     | 7     1     48    |
 *-----------------------------------------------------------*


Embedded chain:

4r1c1 = r1c4 - r2c6 = (4-8)r4c6 = r8c6 - r7c4 = 8r7c1 => -48 r4c1 ; stte

(I don't know why the underlining in the PM??)

[pjb]

Code: Select all

 47      3       2      | 47     9      1      | 8      6      5     
 1478   f1478    148    | 5      6      4-7    | 3      2      9     
 9       6       5      | 3      8      2      | 4      7      1     
------------------------+----------------------+---------------------
d478    e478     9      | 2      5      48     | 1      3      6     
 3       148     148    | 9      7      6      | 5      48     2     
 2       5       6      | 48     1      3      | 9      48     7     
------------------------+----------------------+---------------------
c18      2       7      |b18     4      5      | 6      9      3     
 6       9       148    | 178    3     a78     | 2      5      48     
 5       48      3      | 6      2      9      | 7      1      48     

(7=8)r8c6 - r7c4 = r7c1 - r4c1 = (8-7)r4c2 = r2c2 => -7 r2c6; stte
       \
      r4c6


Phil

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
|f4-7cD   3       2        |e47C     9       1        | 8       6       5        |
| 1478    1478b   148      | 5       6       47       | 3       2       9        |
| 9       6       5        | 3       8       2        | 4       7       1        |
|--------------------------+--------------------------+--------------------------|
|a478     478a    9        | 2       5       48A      | 1       3       6        |
| 3       148     148      | 9       7       6        | 5       48      2        |
| 2       5       6        |d48B     1       3        | 9       48      7        |
|--------------------------+--------------------------+--------------------------|
|b18      2       7        |c18      4       5        | 6       9       3        |
| 6       9       148      | 178     3       78       | 2       5       48       |
| 5       48      3        | 6       2       9        | 7       1       48       |
*--------------------------------------------------------------------------------*

Kraken Row 8 Digit 4 :

8 r4c1 - r7c1 = r7c4 - (8=4) r6c4 - r1c4 = r1c1 - 7 r1c1;

8 r4c2 - 7 r4c2 = r2c2                          - 7 r1c1;

8 r4c6 - (8=4) r6c4 - r1c4 = r1c1               - 7 r1c1; => - 7 r1c1; stte

Leren

[Marty R.]

Code: Select all

+---------------+----------+---------+
| 47   3    2   | 47  9 1  | 8 6  5  |
| 1478 1478 148 | 5   6 47 | 3 2  9  |
| 9    6    5   | 3   8 2  | 4 7  1  |
+---------------+----------+---------+
| 478  478  9   | 2   5 48 | 1 3  6  |
| 3    148  148 | 9   7 6  | 5 48 2  |
| 2    5    6   | 48  1 3  | 9 48 7  |
+---------------+----------+---------+
| 18   2    7   | 18  4 5  | 6 9  3  |
| 6    9    148 | 178 3 78 | 2 5  48 |
| 5    48   3   | 6   2 9  | 7 1  48 |
+---------------+----------+---------+


Play this puzzle online at the Daily Sudoku site


If Leren blesses this I'm done and pleased with the first time using this technique. If he curses it, well, I tried.

ALS XZ rule

(4=87)r48c6

(4=187)r671c4

Z=4, X=7=> -7 r2c6

[eleven]

What a nice MUG, but it doesn't help much (just get r4c1<>4)

Code: Select all

*-------------------------------------------------------------*
 | 47     3       2    | 47    9     1     | 8     6     5     |
 |#148+7 #148+7  #148  | 5     6     47    | 3     2     9     |
 | 9      6      5     | 3     8     2     | 4     7     1     |
 *---------------------+-------------------+-------------------|
 |-478    478    9     | 2     5     48    | 1     3     6     |
 | 3     #148   #148   | 9     7     6     | 5     48    2     |
 | 2      5      6     | 48    1     3     | 9     48    7     |
 *---------------------+-------------------+-------------------|
 |#18     2      7     |#18    4     5     | 6     9     3     |
 | 6      9     #148   |#18+7  3     78    | 2     5    #48    |
 | 5     #48     3     | 6     2     9     | 7     1    #48    |
 *-------------------------------------------------------------*

[bat999]

Code: Select all

.------------------.---------------.-----------.
| *47    3     2   | *47   9   1   | 8  6   5  |
|  1478  1478  148 |  5    6  *47  | 3  2   9  |
|  9     6     5   |  3    8   2   | 4  7   1  |
:------------------+---------------+-----------:
| *478   478   9   |  2    5  *8-4 | 1  3   6  |
|  3     148   148 |  9    7   6   | 5  48  2  |
|  2     5     6   | *48   1   3   | 9  48  7  |
:------------------+---------------+-----------:
| *18    2     7   | *18   4   5   | 6  9   3  |
|  6     9     148 |  178  3   78  | 2  5   48 |
|  5     48    3   |  6    2   9   | 7  1   48 |
'------------------'---------------'-----------'

(4)r4c6 - (4)r4c1
(4)r4c6 - (4=7)r2c6 - r1c4 = r1c1 - (7)r4c1
(4)r4c6 - (4=8)r6c4 - r7c4 = r7c1 - (8)r4c1
=> -4 r4c6; stte

That was the best I could come up with.
Very difficult for what looks like a simple puzzle.
But I don't feel so bad now I've seen the other solutions posted above.


The other possible way I wanted to use was something like this...

(4)r4c6 - (4=7)r2c6 - r1c4 = (7)r1c1
(4)r4c6 - (4=8)r6c4 - r7c1 = (8)r7c1
(78)r17c1 - (78=4)r4c1 - (4)r4c6
In effect, a Type 1 Discontinuous Nice Loop (if r4c6 is 4 then r4c6 can't be 4).
But I don't know how to express it properly.

[eleven]

This is a 3-way deduction. Basically AIC's and nice loops only handle 2-way (OR) deductions.
So AIC writers would write it as "Kraken", a 3 way starting with 4,7,and 8 in r4c1, showing that all lead to r4c6<>4 (thus avoiding the embarrassing contradiction), see Leren's solution.
Also look at Steve's solution, who writes 2 kites in one "embedded chain".

Yes, every normal manual solver would take the 2 kites, one by one. A simple puzzle, but a challenge for a 1-stepper (formulation).

[bat999]

...So AIC writers would write it as "Kraken", a 3 way starting with 4,7,and 8 in r4c1, showing that all lead to r4c6<>4...

Yes, that's the way to do it.
Kraken Cell r4c1 :
(4)r4c1 - (4)r4c6
(7)r4c1 - r1c1 = r1c4 - (7=4)r2c6 - (4)r4c6
(8)r4c1 - r7c1 = r7c4 - (8=4)r6c4 - (4)r4c6
=> -4 r4c6; stte

[DonM]

I continue to wonder why the term 'nice loop' continues to be used as if it is a technique rather than a notation. Like it or not, Eureka AIC notation is in use here. Under the latter notation, a chain can be said to be discontinuous if there is a discontinuity. That's it, not (like) a Type this or that nice loop.

[ronk]

I continue to wonder why the term 'nice loop' continues to be used as if it is a technique rather than a notation. Like it or not, Eureka AIC notation is in use here. Under the latter notation, a chain can be said to be discontinuous if there is a discontinuity. That's it, not (like) a Type this or that nice loop.

Wouldn't think many people on this thread look at XSUDO, but XSUDO lists Discontinuous Nice Loop as a technique.

Discontinuous is an adjective, but we can have a discontinuous chain? Seems oxymoronic to me.

[DonM]

I continue to wonder why the term 'nice loop' continues to be used as if it is a technique rather than a notation. Like it or not, Eureka AIC notation is in use here. Under the latter notation, a chain can be said to be discontinuous if there is a discontinuity. That's it, not (like) a Type this or that nice loop.

Wouldn't think many people on this thread look at XSUDO, but XSUDO lists Discontinuous Nice Loop as a technique.

Discontinuous is an adjective, but we can have a discontinuous chain? Seems oxymoronic to me.

Even if I didn't know anything about sudoku, a discontinuous loop would sound more oxymoronic. Semantically, a loop infers continuity; a chain doesn't.

Fwiw: I don't consider Xsudo an authoritative source on sudoku definitions.

[ronk]

I continue to wonder why the term 'nice loop' continues to be used as if it is a technique rather than a notation. Like it or not, Eureka AIC notation is in use here. Under the latter notation, a chain can be said to be discontinuous if there is a discontinuity. That's it, not (like) a Type this or that nice loop.

Wouldn't think many people on this thread look at XSUDO, but XSUDO lists Discontinuous Nice Loop as a technique.

Discontinuous is an adjective, but we can have a discontinuous chain? Seems oxymoronic to me.

Even if I didn't know anything about sudoku, a discontinuous loop would sound more oxymoronic. Semantically, a loop infers continuity; a chain doesn't.

Fwiw: I don't consider Xsudo an authoritative source on sudoku definitions.

Myth Jellies did the Sudoku community a disservice by using the same loop term used earlier by Jeff. Early on Myth was careful in a very few spots to write AIC loop where the Eureka crowd casually writes loop today.

DonM, you need to occasionally remind yourself that unless there is either a discontinuous (or continuous) loop of alternating inferences, there is no deduction, no exclusion, no inclusion. Here I use loop in the more general sense, as did Jeff, meaning the inference stream properly ends where it began, properly ends where it began.

[David P Bird]

No-one can copyright such a basic word as 'loop'. Nice Loops are geographic; they follow a chain of inferences until they return to the start point. AIC loops are logical; they are only made when a circuit of alternating inferences is completed, otherwise they simply remain as open ended chains.

Because Nice Loops only show the inferences for the linking digits between cell groups while AICs require all inferences to be shown, their elimination rules are different. For simple chains Nice Loop notations are shorter but they require more elimination rules depending on their construction, whereas AIC notations will be longer but have a much simpler set of elimination rules. Another, perhaps minor, issue is that AICs were designed to be bidirectional whereas Nice Loops were not.

There is no confusion regarding how the 'loop' term is being used if players choose to notate and discuss their deductions either as Nice Loops or as AICs. However it is the players who explain their eliminations using Nice Loop logic and terms while using AIC notation conventions who do the community a great disservice. In particular a 'continuous loop' in AIC terminology seems to be a 'type 2 discontinuous loop' in NL terminology. The confusion this mix and match approach causes is further compounded by the style issues regarding the best way to notate different situations which affects both systems.

Like it or not, our solutions now include many more sub-pattern inferences and these can be notated more easily using AIC disciplines than Nice Loop ones.

Looking at the history of different academic topics, the way they were described by the pioneers has often proved inadequate to cover the extensions they lead on to. At the birth of calculus Newton used 'fluxions' and Leibniz used 'infinitesimal change' to describe what we now call 'differentials' but it doesn't mean we don't still honour their contributions.

I must stop now as my candle has almost burnt down.

TAGdpbNotation

[ronk]

No-one can copyright such a basic word as 'loop'. Nice Loops are geographic; they follow a chain of inferences until they return to the start point. AIC loops are logical; they are only made when a circuit of alternating inferences is completed, otherwise they simply remain as open ended chains.

From a progammer's point of view then, what are the rules to determine if an elimination exists for both the AIC loop case and the "open-ended" chain case?