The New Sudoku Players' Forum

[m_b_metcalf]

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 . . . 7 6 5 . . .
 . . 7 . . . 3 . .
 . 4 . . . . . 1 .
 5 . . . . . . . .
 3 . . . . . . . .
 8 . . . . . . . .
 . 1 . . . . . 2 .
 . . 3 . . . 4 . .
 . . . 2 7 6 . . .   quite hard

 . . . 5 3 4 . . .
 . . 6 . . . 3 . .
 . 3 . . . . . 1 .
 4 . . . . . . . .
 7 . . . . . . . .
 6 . . . . . . . .
 . 8 . . . . . 2 .
 . . 7 . . . 1 . .
 . . . 6 5 3 . . .   moderate

[Leren]

Hi Mike,

Did you have the puzzle labels the wrong way around ? The "moderate" one was harder than the "quite hard one", which solved with basics.

Leren

[m_b_metcalf]

Did you have the puzzle labels the wrong way around ? The "moderate" one was harder than the "quite hard one", which solved with basics.

Well, the fount of all wisdom, SukakuExplainer, says:

Code: Select all

...765.....7...3...4.....1.5........3........8.........1.....2...3...4.....276...   ED=7.9/1.2/1.2   
...534.....6...3...3.....1.4........7........6.........8.....2...7...1.....653...   ED=4.3/1.2/1.2   


and uses lots of Nishio Forcing Chains for the first one. I'm puzzled (excuse the pun).
Regards,

Mike

[Leren]

My mistake. I was multi-tasking and somehow loaded an easy puzzle instead of the intended hard one.

I think SE must have some tricks I haven't included yet. Would be interested in the SE solution path for the easy puzzle. I tried it in Andrew Stuart's solver and it solved about the same way I did.

Leren

[m_b_metcalf]

Would be interested in the SE solution path for the easy puzzle.

This was the best I could get:

Code: Select all

Analysis results
Difficulty rating: 4.3 (Grouped Skyscraper 216)
This X Sudoku can be solved using the following logical methods:
58 x Hidden Single
1 x Direct Pointing
5 x Direct Hidden Pair
18 x Generalized Intersections
1 x Hidden Pair
1 x (2 Strong Links) X-Loop 056
1 x Grouped Skyscraper 216
The most difficult technique (ER): Grouped Skyscraper 216

Regards,

Mike

[Leren]

Hi Mike, this is my pm after I had exhausted the first round of intersections and used a diagonal based X Wing (hopefully the X-Loop 056).

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*--------------------------------------------------------------------------------*
| 1289    7       129      | 5       3       4        | 89      6       289      |
| 289     45      6        | 12789   12789   12789    | 3       45789   24789    |
| 289     3       45       | 2789    2789    6        | 45789   1       24789    |
|--------------------------+--------------------------+--------------------------|
| 4       259     2589     | 12789   6       12789    | 25789   5789    3        |
| 7       129     3        | 12489   289     5        | 2489    489     6        |
| 6       259     2589     | 3       24789   2789     | 245789  45789   1        |
|--------------------------+--------------------------+--------------------------|
| 3       8       49       | 1479    1479    179      | 6       2       5        |
| 5       6       7        | 2489    2489    289      | 1       3       49       |
| 129     1249    1249     | 6       5       3        | 4789    4789    789      |
*--------------------------------------------------------------------------------*

Is there anything that SE has removed and/ or where is the Grouped Skyscraper. I'm guessing that it may have a diagonal base.

Leren

[m_b_metcalf]

Hi Mike, this is my pm after I had exhausted the first round of intersections and used a diagonal based X Wing (hopefully the X-Loop 056).
[snip]
Is there anything that SE has removed and/ or where is the Grouped Skyscraper. I'm guessing that it may have a diagonal base.

Leren,
SE has two 4.3 steps, separated by a single. The gory details are hidden below.

HTH

Mike

P.s. For testing purposes, you might find this hidden set useful.

Hidden Text: Show

Code: Select all

+----------------------+----------------------+----------------------+
| 1289   7      129    | 5      3      4      | 89     6      289    |
| 289    45     6      | 12789  12789  12789  | 3      45789  24789  |
| 289    3      45     | 2789   2789   6      | 45789  1      24789  |
+----------------------+----------------------+----------------------+
| 4      1259   12589  | 12789  6      12789  | 25789  5789   3      |
| 7      129    3      | 12489  289    5      | 2489   489    6      |
| 6      259    2589   | 3      24789  2789   | 245789 45789  1      |
+----------------------+----------------------+----------------------+
| 3      8      49     | 1479   1479   179    | 6      2      5      |
| 5      6      7      | 2489   2489   289    | 1      3      49     |
| 129    1249   1249   | 6      5      3      | 4789   4789   789    |
+----------------------+----------------------+----------------------+

(2 Strong Links) X-Loop 056

This technique relies on Conjugate Pairs that infer a strong link and/or
a special arrangement of values in a line or block also known as Grouped
Strong Links (where a strong link is inferred from groups of cells having
the same value) that form a loop (an X-Loop). These use strong links in
Location inferred from 1 value (L1), therefore, L1-Ring can be used to
describe this loop (Currently, L1 is reserved for 3 strong links).

the arrangement of cells with value 1 in Main Diagonal and Anti Diagonal
(Green outlined region) form strong links (conjugate pairs, shown as
green values) or grouped strong links (orange cell outline or yellow
cell background). These strong links are weakly linked to each other
via row 4, row 4 and column A (Red outlined region) forming a loop/ring.

Any occurrence of the value 1 can therefore be removed from any cells
sharing a region or regions with ALL cells with value 1 in ANY of row 4,
row 4 or column A outside of Main Diagonal and Anti Diagonal.
This technique is part of more generalized technique called X-chains
which in itself is part of more generalized technique called Alternating
Inference Chains (AIC).

This technique can also be described as Mutant X-Wing d\d/\r4c1.

The grouped strong link when inferred from cells in a block that are
 arranged in one mini-row and one mini-column is also known commonly
as "Empty rectangle".

The inference of a strong link from a group of cells with value 1 in
any region can be spotted when a an "Empty mini Area (EmA)" is observed.
This EmA could be an empty mini-Line (EmL) in a region or regions.
In the case of "Empty rectangle" the EmA is a group of empty cells
that can also be referred to as "Empty mini Rectangle (EmR)".

+----------------------+----------------------+----------------------+
| 1289   7      129    | 5      3      4      | 89     6      289    |
| 289    45     6      | 12789  12789  12789  | 3      45789  24789  |
| 289    3      45     | 2789   2789   6      | 45789  1      24789  |
+----------------------+----------------------+----------------------+
| 4      259    2589   | 12789  6      12789  | 25789  5789   3      |
| 7      1      3      | 2489   289    5      | 2489   489    6      |
| 6      259    2589   | 3      24789  2789   | 245789 45789  1      |
+----------------------+----------------------+----------------------+
| 3      8      49     | 1479   1479   179    | 6      2      5      |
| 5      6      7      | 2489   2489   289    | 1      3      49     |
| 129    249    1249   | 6      5      3      | 4789   4789   789    |
+----------------------+----------------------+----------------------+

Grouped Skyscraper 216

This technique relies on Conjugate Pairs that infer a strong link
and/or a special arrangement of values in a line or block also known
as Grouped Strong Links (where a strong link is inferred from groups
 of cells having the same value). These use strong links in Location
inferred from 1 value (L1), therefore, Grouped L1-Wing can be used
to describe this pattern.(Currently, L1 is reserved for 3 strong links).

the arrangement of cells with value 7 in column I and Anti Diagonal
form strong links (conjugate pairs, shown as green values) or grouped
strong links (orange cell outline or yellow cell background).
These strong links are weakly linked to each other via block 3 and
 block 3 (Red or Green outlined region).

Any occurrence of the value 7 can therefore be removed from any cells
sharing a region or regions with ALL cells with value 7 in column I
and Anti Diagonal that are not part of block 3 or block 3.
This technique is part of more generalized technique called X- chains
which in itself is part of more generalized technique called Alternating
Inference Chains (AIC).

This technique uses logic closely related to Finned X-Wing technique logic.

The grouped strong link when inferred from cells in a block that are
arranged in one mini-row and one mini-column is also known commonly
as "Empty rectangle".

The inference of a strong link from a group of cells with value 7 in
any region can be spotted when a an "Empty mini Area (EmA)" is observed.
This EmA could be an empty mini-Line (EmL) in a region or regions.
In the case of "Empty rectangle" the EmA is a group of empty cells
that can also be referred to as "Empty mini Rectangle (EmR)".

[Leren]

The X Loop 056 I already had in my bag of tricks but this was a special case with 1 extra elimination that I'd missed, so all I had to do was correct a deficiency.

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*--------------------------------------------------------------*
|a1289 7     129    | 5      3      4     | 89     6     289   |
| 289  45    6      | 12789  12789  12789 | 3      45789 24789 |
| 289  3     45     | 2789   2789   6     | 45789  1     24789 |
|-------------------+---------------------+--------------------|
| 4    259-1 2589-1 |b12789  6     c12789 | 25789  5789  3     |
| 7    129   3      | 2489-1 289    5     | 2489   489   6     |
| 6    259   2589   | 3      24789  2789  | 245789 45789 1     |
|-------------------+---------------------+--------------------|
| 3    8     49     | 1479   1479   179   | 6      2     5     |
| 5    6     7      | 2489   2489   289   | 1      3     49    |
|d129  1249  1249   | 6      5      3     | 4789   4789  789   |
*--------------------------------------------------------------*

The extra elimination that I'd missed was -1 r5c4. When added it brings us to here.

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*------------------------------------------------------------*
| 1289 7   129  | 5      3      4     | 89      6      289   |
| 289  45  6    | 12789  12789  12789 | 3      c45789 b24789 |
| 289  3   45   | 2789   2789   6     |c45789   1     b24789 |
|---------------+---------------------+----------------------|
| 4    259 2589 | 1289-7 6     d12789 | 25789   5789   3     |
| 7    1   3    | 2489   289    5     | 2489    489    6     |
| 6    259 2589 | 3      24789  289-7 | 245789  45789  1     |
|---------------+---------------------+----------------------|
| 3    8   49   | 1479   1479   179   | 6       2      5     |
| 5    6   7    | 2489   2489   289   | 1       3      49    |
| 129  249 1249 | 6      5      3     | 4789    4789  a789   |
*------------------------------------------------------------*

(7) r9c9 = r12c9 - r2c8, r3c7 = (7) r4c6 => - 7 r4c4, r6c6

This was certainly new for me and has two grouped strong links, but what is it ? I'm inclined to call it a Column / Anti diagonal Kite rather than a Skyscraper.

Importantly, as in a normal Kite, the intersection cell in the Kite box must not have a 7 and the column must only have a single 7 outside of the Kite box, just like normal Kites. In theory you could have 3 7's on the Anti Diagonal in Box 5 and get 3 eliminations. I've also coded for additional cases so it works for all directions.

For me that solved the whole puzzle, only a few intersections were needed to finish.

Leren

[Pat]

Code: Select all

*------------------------------------------------------------*
| 1289 7   129  | 5      3      4     | 89      6      289   |
| 289  45  6    | 12789  12789  12789 | 3      c45789 b24789 |
| 289  3   45   | 2789   2789   6     |c45789   1     b24789 |
|---------------+---------------------+----------------------|
| 4    259 2589 | 1289-7 6     d12789 | 25789   5789   3     |
| 7    1   3    | 2489   289    5     | 2489    489    6     |
| 6    259 2589 | 3      24789  289-7 | 245789  45789  1     |
|---------------+---------------------+----------------------|
| 3    8   49   | 1479   1479   179   | 6       2      5     |
| 5    6   7    | 2489   2489   289   | 1       3      49    |
| 129  249 1249 | 6      5      3     | 4789    4789  a789   |
*------------------------------------------------------------*

(7) r9c9 = r12c9 - r2c8, r3c7 = (7) r4c6 => - 7 r4c4, r6c6

This has two grouped strong links, but what is it ? I'm inclined to call it a Column / Anti diagonal Kite rather than a Skyscraper.

Importantly, as in a normal Kite, the intersection cell in the Kite box must not have a 7 and the column must only have a single 7 outside of the Kite box, just like normal Kites.

Leren

yes, a kite.


= a "finned" X-wing:

base houses are c9 + anti-diagonal
(★ required: no 7 in base-intersect)

cover houses are b3 + diagonal

"fin" = r4c6


-or- cover = b35
"fin" = r9c9

[thelardoffear]

From the above position my solver found a couple of very short Nishio eliminations:

(R5C5) is not 2 - Nishio: (from R5C5=2 => R1C3=2 => No possible positions for 2 in Vertical Column 1)
(R5C5) is not 8 - Nishio: (from R5C5=8 => R1C7=8 => No possible positions for 8 in Vertical Column 9)

[Leren]

Code: Select all

 .  .  . |  .  .  . |  .  X  X 
 .  .  . |  .  .  . |  .  /  .
 .  .  . |  .  .  . |  X  X  .
---------+----------+----------
 .  .  . |  *  .  X |  .  /  . 
 .  .  . |  .  X  . |  .  /  . 
 .  .  . |  X  .  * |  .  /  .   
---------+----------+----------   
 .  .  / |  .  .  . |  .  /  .   
 .  /  . |  .  .  . |  .  X  .   
 /  .  . |  .  .  . |  .  /  .


The above is an exemplar for the SE 245 move.   / = must not contain X    . = may or not contain X    * potential eliminations of X

The only provisos arethat at least one of r1c9 or r3c7 and one of r4c6 or r6c4 has an X and at least one of r4c6, r5c6 and r6c4 has an X.

Leren

[Pat]

r5c5 should be marked "X".
(not "*"; and not "*X".)

no exclusion at r5c5.

[Leren]

HI Pat. You were right. Made changes. Leren