The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |.5.|...|18.|
 |8..|.1.|..4|
 |.9.|..6|5..|
 |---+---+---|
 |...|49.|.1.|
 |5.8|...|9.7|
 |.4.|.87|...|
 |---+---+---|
 |..1|9..|.5.|
 |9..|.3.|..8|
 |.73|...|.9.|
 *-----------*


Play/Print this puzzle online

[SpAce]

Code: Select all

.--------------------.--------------------.----------------------.
|t267     5    t2467 |se237   r247   e234 |   1     8      9     |
| 8       3    u27   |  5      1      9   |oaA267*  267    4     |
| 1       9    u247  |  8     r247    6   |   5     237  iB2(3)  |
:--------------------+--------------------+----------------------:
|g2367  vh26  vh267  |  4      9      5   |   8     1    vi2(3)6 |
| 5       1     8    | e236    26    e23  |   9     4      7     |
|g236     4     9    |  1      8      7   |  b236   236    5     |
:--------------------+--------------------+----------------------:
|f26      8     1    |  9    qc2467  f24  | pb2367  5      26-3  |
| 9       26    5    | d267    3      1   |   4     267    8     |
| 4       7     3    |dc26     5      8   |  b26    9      1     |
'--------------------'--------------------'----------------------'


Kraken Cell (267)r2c7

(2)r2c7 - (2=3)r3c9
||
(6)r2c7 - (6=372)r679c7 - (7)r6c5|(2)r9c4 = (67)r89c4 - (6|7=UR=4)r15c36 - (4=26)r7c61 - r46c1 = r4c23 - (6=23)r43c9
||
(7)r2c7 - r7c7 = r7c5 - r13c5 = r1c4 - r1c13 = r23c3 - (7=263)r4c239

=> -3 r7c9; stte

[Cenoman]

Code: Select all

 +---------------------+---------------------+---------------------+
 |  267    5    2467   |  237   247    234   |  1      8     9     |
 |  8      3    27     |  5     1      9     |  267   b267   4     |
 |  1      9    247    |  8     24-7   6     |  5     a237*  23    |
 +---------------------+---------------------+---------------------+
 |  2367  c26^  267    |  4     9      5     |  8      1    d236   |
 |  5      1    8      |  236   26     23    |  9      4     7     |
 |  236    4    9      |  1     8      7     |  236   c236^  5     |
 +---------------------+---------------------+---------------------+
 |  26     8    1      |  9   ga2467*  24    |fa2367*  5    e236   |
 |  9     c26^  5      |  267   3      1     |  4    ca267*^ 8     |
 |  4      7    3      |  26    5      8     |  26     9     1     |
 +---------------------+---------------------+---------------------+

With almost kite (7)r7c5=r7c7-r8c8=r3c8 + rfr2c8 and almost skyscraper (6)r6c8=r8c8-r8c2=r4c2 + rfr2c8

[Kite(7)r7c5=r7c7-r8c8=r3c8] = (7-6)r2c8 = [SS(6)r6c8=r8c8-r8c2=r4c2] - (6)r4c9 = (6-3)r7c9 = (3-7)r7c7 = (7)r7c5 => -7 r3c5; lclste

[SpAce]

With almost kite (7)r7c5=r7c7-r8c8=r3c8 + rfr2c8 and almost skyscraper (6)r6c8=r8c8-r8c2=r4c2 + rfr2c8
[Kite(7)r7c5=r7c7-r8c8=r3c8] = (7-6)r2c8 = [SS(6)r6c8=r8c8-r8c2=r4c2] - (6)r4c9 = (6-3)r7c9 = (3-7)r7c7 = (7)r7c5 => -7 r3c5; lclste

Beautiful!

[eleven]

Nice, Cenoman !

Not a one-stepper, but an interesting pattern (5-link 26, easy chain, grouped skyscraper) leaving singles only.

Code: Select all

 *------------------------------------------------*
 | .    .   .     | .    .   .   | .    .    .    |
 | .    .   .     | .    .   .   | .    .    .    |
 | .    .   .     | .    .   .   | .    .    2-3  |
 |----------------+--------------+----------------|
 | .    .   .     | .    .   .   | .    .    236  |
 | .    .   .     | .    .   .   | .    .    .    |
 | 236  .   .     | .    .   .   | 236  23-6 .    |
 |----------------+--------------+----------------|
 | 2-6  .   .     | .    .   .   | .    .    236  |
 | .    .   .     | .    .   .   | .    .    .    |
 | .    .   .     | .    .   .   | 26   .    .    |
 *------------------------------------------------*

[SpAce]

Not a one-stepper, but an interesting pattern (5-link 26, easy chain, grouped skyscraper) leaving singles only.

Could you dumb that down a bit?

[eleven]

Code: Select all

 *-------------------------------------------------*
 |  .    .   .     | .    .   .   | .    .    .    |
 |  .    .   .     | .    .   .   | .    .    .    |
 |  .    .   .     | .    .   .   | .    .    2-3  |
 |-----------------+--------------+----------------|
 |  .    .   .     | .    .   .   | .    .   *26+3 |
 |  .    .   .     | .    .   .   | .    .    .    |
 | *26+3 .   .     | .    .   .   |*263 *263  .    |
 |-----------------+--------------+----------------|
 | *26   .   .     | .    .   .   | .    .   *26+3 |
 |  .    .   .     | .    .   .   | .    .    .    |
 |  .    .   .     | .    .   .   | 26   .    .    |
 *-------------------------------------------------*

5-link DP 26: 3r47c9==3r6c1 - r6c78 = r4c9 => -3r3c9

Code: Select all

 *-------------------------------------------------*
 |  .    .   .     | .    .   .   | .    .    .    |
 |  .    .   .     | .    .   .   | .    .    .    |
 |  .    .   .     | .    .   .   | .    .   d23   |
 |-----------------+--------------+----------------|
 |  .    .   .     | .    .   .   | .    .   d236  |
 |  .    .   .     | .    .   .   | .    .    .    |
 | a236  .   .     | .    .   .   |a236  23-6 .    |
 |-----------------+--------------+----------------|
 | b26   .   .     | .    .   .   | .    .   c236  |
 |  .    .   .     | .    .   .   | .    .    .    |
 |  .    .   .     | .    .   .   |b26   .    .    |
 *-------------------------------------------------*

(6=2)r6c17 - (2=6)r7c1|r9c7 - r7c9 = r34c9 => -6r6c8

Code: Select all

 *-------------------------------------------------*
 |  .    .   .     | .    .   .   | .    .    .    |
 |  .    .   .     | .    .   .   | .    .    .    |
 |  .    .   .     | .    .   .   | .    .   c23   |
 |-----------------+--------------+----------------|
 |  .    .   .     | .    .   .   | .    .   c236  |
 |  .    .   .     | .    .   .   | .    .    .    |
 | a236  .   .     | .    .   .   |b236 b236  .    |
 |-----------------+--------------+----------------|
 |  2-6  .   .     | .    .   .   | .    .   d236  |
 |  .    .   .     | .    .   .   | .    .    .    |
 |  .    .   .     | .    .   .   | 26   .    .    |
 *-------------------------------------------------*

6r6c1 = r6c78 - r34c9 = r7c9 => -6r7c1

[Edit: added missing digit, thx SpAce ]

[SpAce]

Thanks for the clarifications, eleven!

5-link DP 26: 3r4c9==3r6c1 - r6c78 = r4c9 => -3r3c9

So it's not a uniqueness-related DP but rather a double-oddagon (using internal guardians) or something? Or am I still missing something? I originally paid attention to this formation myself, but couldn't see this possibility of using it (was looking for a uniqueness pattern instead). Now I do, thanks for that! (Possible typo: first node -> 3r47c9 ?)

(6=2)r6c17 - (2=6)r7c1|r9c7 - r7c9 = r34c9 => -6r6c8

Very nice! At my level that's not called an "easy chain" Sure, it's very elegant and easy to understand when shown, but I doubt that discovering such things is covered in Chaining 101. I'm always happy to see clever things like these (and have learned to expect them from you), but I'm not sure if I'll ever start spotting them myself.

6r6c1 = r6c78 - r34c9 = r7c9 => -6r7c1

This one was trivial, of course.

(In the last two chains r34c9 could be just r4c9, right?)

[Cenoman]

I had explored 5-link DP(26)r4c29,r7c9,r8c28 but needed nets. eleven's elegant results with another (26)DP made me dig on the idea.
Here another one (one step, simple chain):

Code: Select all

 +---------------------+---------------------+---------------------+
 | e267    5    2467   | d237   247    234   |  1      8     9     |
 |  8      3    27     |  5     1      9     |  267    267   4     |
 |  1      9    247    |  8     247    6     |  5      237   23    |
 +---------------------+---------------------+---------------------+
 | f2367   26   267    |  4     9      5     |  8      1    g236   |
 |  5      1    8      |  236   26     23    |  9      4     7     |
 | a236*   4    9      |  1     8      7     |  26-3  a236*  5     |
 +---------------------+---------------------+---------------------+
 |  26*    8    1      |  9     2467   24    |  2367   5     236   |
 |  9      26*  5      | c267   3      1     |  4     b267*  8     |
 |  4      7    3      |  26    5      8     |  26     9     1     |
 +---------------------+---------------------+---------------------+

5-link DP(26)r6c18,r7c1,r8c28 using internals
(3)r6c18==(7)r8c8 - r8c4 = r1c4 - r1c1= (7-3)r4c1 = (3)r4c9 => -3 r6c7; ste

[eleven]

Very nice again, Cenoman.

(In the last two chains r34c9 could be just r4c9, right?)

In the puzzle, yes, here it makes clear, that there is a strong link.
Thx for pointing out the missing row number.

[SpAce]

5-link DP(26)r6c18,r7c1,r8c28 using internals
(3)r6c18==(7)r8c8 - r8c4 = r1c4 - r1c1= (7-3)r4c1 = (3)r4c9 => -3 r6c7; ste

Awesome! Does that kind of a DP have a more specific name? I think it would be helpful, because at first glance it looks like a uniqueness DP (having multiple digits and allowing internal guardians) but it actually works like an oddagon. How about something like "Remote-pair Oddagon"? Does any thread list all known DP types?

[Cenoman]

Thank you eleven, SpAce and SteveC !

I kept the name "5-link DP" used by eleven, as I found it relevant.
Nevertheless using DP might be confusing, unless it is clear that DP refers to two different types of patterns:

- patterns with more than one solutions: typically UR, BUG and BUG-lite, all patterns addressed here. All these patterns are based on uniqueness hypothesis.

- patterns with no solution at all: typically oddagon and this "5-link DP" (but there are others, I remember having read an eleven's solution based on a more complex one). These patterns are not based on uniqueness hypothesis. Contrarywise, they are based on "the puzzle has at least one solution".

The 5-link DP has already been addressed in this thread
Two names were proposed then: "Odd bivalue loop" or "Bivalue oddagon". SpAce thinks of Remote-pair oddagon.
I thought of "Naked pair broken wing" or "Bivalue broken wing". Finally I would chose "Bivalue oddagon".

SpAce noted that this type of DP allows internal guardians. From pure logic point of view, internal guardians are not forbidden for the single digit n-link oddagon. The n candidates can't all be true, and this could be demonstrated using internals as well. But... you will have at least n internals (in the best case of n bivalue cells) of diverse digits. Such a solution is very likely to win "the best obfuscation award" (expression borrowed to SteveC) !

[SpAce]

Thanks, Cenoman! That was very helpful.

Nevertheless using DP might be confusing, unless it is clear that DP refers to two different types of patterns:
- patterns with more than one solutions:
- patterns with no solution at all:

Exactly. My point was that it would be clearer if these two types of DPs had distinctive names.

typically oddagon and this "5-link DP" (but there are others, I remember having read an eleven's solution based on a more complex one).

Could someone find any examples? This is an interesting topic!

The 5-link DP has already been addressed in this thread

Thanks, I hadn't seen (or registered) that before.

Two names were proposed then: "Odd bivalue loop" or "Bivalue oddagon". SpAce thinks of Remote-pair oddagon.
I thought of "Naked pair broken wing" or "Bivalue broken wing". Finally I would chose "Bivalue oddagon".

Me too. I think that's a good name. It also scales to structures with more digits. For example, I came up with this theoretical 7-link grouped "trivalue oddagon":

Code: Select all

.----------------.-----------------.----------------.
|     a123       |      g123       |                |
|                |f123             |                |
|                |f123             |                |
:----------------+-----------------+----------------:
|     b123       |                 |                |
|           c123 |      d123  d123 |                |
|     b123       |e123             |                |
:----------------+-----------------+----------------:
|                |                 |                |
|                |                 |                |
|                |                 |                |
'----------------'-----------------'----------------'

Assuming it works as I thought, has anyone seen that in a real puzzle? Are even larger digit groups possible?

SpAce noted that this type of DP allows internal guardians. From pure logic point of view, internal guardians are not forbidden for the single digit n-link oddagon.

Indeed. I realized that myself a bit after posting that. As you noted, it wouldn't be very practical, though.