The New Sudoku Players' Forum

[SteveG48]

Code: Select all

 *-----------*
 |...|...|..7|
 |48.|15.|..3|
 |...|6.4|.2.|
 |---+---+---|
 |56.|...|..2|
 |..8|.6.|7..|
 |7..|...|.45|
 |---+---+---|
 |.2.|5.3|...|
 |9..|.21|.34|
 |1..|...|...|
 *-----------*


[shye]

Edit: contains a mistake, scroll down to see the missed case and the additional logic that amends it

Code: Select all

,---------------,-----------------,-------------,
| 6 #159   1259 | 2389  389   289 | 4  #15   7  |
| 4  8     27   | 1     5     27  | 9   6    3  |
| 3 *1579 *1579 | 6    *789   4   | 58  2    18 |
:---------------+-----------------+-------------:
| 5  6     149  | 479   1479  79  | 3   8    2  |
| 2  34    8    | 34    6     5   | 7  #19   19 |
| 7  139   139  | 2389  1389  289 | 6   4    5  |
:---------------+-----------------+-------------:
| 8  2     47   | 5    *479   3   | 1  *79   6  |
| 9  7-5   6    | 78    2     1   | 58  3    4  |
| 1 *3457 *3457 | 4789  4789  6   | 2  *579  89 |
'---------------'-----------------'-------------'

r1c2, r1c8, r5c8 form a remote triple due to weakly linked 9s (r1c2 - r3c23 = r3c5 - r7c5 = r7c8 - r5c8)
this combines with the positions for 5 in r9 to form a finned x-wing
=> -5r8c2 stte

XSudo Input: Show

6 Truths = {5R9 9R37 1N2 15N8}
9 Links = {15r1 5c2 9c5 159c8 5b7 9b1}

[Cenoman]

Code: Select all

 +---------------------+----------------------+------------------+
 |  6    159*  e1259#  |  2389   389    289   |  4    15*   7    |
 |  4    8     f27     |  1      5     g27    |  9    6     3    |
 |  3   d1579#  1579   |  6     g79     4     |  58*  2     18   |
 +---------------------+----------------------+------------------+
 |  5    6      149    |  479    1479   79    |  3    8     2    |
 |  2    34     8      |  34     6      5     |  7    19    19   |
 |  7    139    139    |  2389   1389   289   |  6    4     5    |
 +---------------------+----------------------+------------------+
 |  8    2      47     |  5     h479    3     |  1    79    6    |
 |  9   c57*    6      |  78     2      1     | b58*  3     4    |
 |  1   d3457#  3457   | i4789  h4789   6     |  2    579  a8-9  |
 +---------------------+----------------------+------------------+

5-link oddagon (5)r18, c27, b3 having three guardians:
(8)r9c9 = (8-5)r8c7 = r8c2 - (5)r39c2 == (5-2)r1c3 = r2c3 - (2=79)b2p68 - r79c5 = (9)r9c4 => -9 r9c9; ste

[Ngisa]

Code: Select all

+-------------------+---------------------+-----------------+
| 6   d159     1259 | 2389    389     289 | 4     15     7  |
| 4    8       27   | 1       5       27  | 9     6      3  |
| 3   d1579  ed1579 | 6      c7*9     4   |f58    2      1-8|
+-------------------+---------------------+-----------------+
| 5    6       149  | 479     1479    79  | 3     8      2  |
| 2    34      8    | 34      6       5   | 7     19     19 |
| 7    139     139  | 2389    1389    289 | 6     4      5  |
+-------------------+---------------------+-----------------+
| 8    2       47   | 5      c479     3   | 1    a79     6  |
| 9   c5*7     6    | 78      2       1   | 58    3      4  |
| 1   b3457   b3457 |b4789   b4789    6   | 2    a579   a89 |
+-------------------+---------------------+-----------------+


(8=975)b9p928 - [(5,9)r9c23,r9c45] = [(5*)r8c2,(97*)r73c5] - [(7)r3c23,(5)r13c2] = (5)r3c3 - (5=8) => - 8r3c9; stte

Clement

[Cenoman]

Code: Select all

,---------------,-----------------,-------------,
| 6 #159   1259 | 2389  389   289 | 4  #15   7  |
| 4  8     27   | 1     5     27  | 9   6    3  |
| 3 *1579 *1579 | 6    *789   4   | 58  2    18 |
:---------------+-----------------+-------------:
| 5  6     149  | 479   1479  79  | 3   8    2  |
| 2  34    8    | 34    6     5   | 7  #19   19 |
| 7  139   139  | 2389  1389  289 | 6   4    5  |
:---------------+-----------------+-------------:
| 8  2     47   | 5    *479   3   | 1  *79   6  |
| 9  7-5   6    | 78    2     1   | 58  3    4  |
| 1 *3457 *3457 | 4789  4789  6   | 2  *579  89 |
'---------------'-----------------'-------------'

r1c2, r1c8, r5c8 form a remote triple due to weakly linked 9s (r1c2 - r3c23 = r3c5 - r7c5 = r7c8 - r5c8)
this combines with the positions for 5 in r9 to form a finned x-wing
=> -5r8c2 stte

XSudo Input: Show

6 Truths = {5R9 9R37 1N2 15N8}
9 Links = {15r1 5c2 9c5 159c8 5b7 9b1}

Hi shye,
I'm in a trouble with your assertion

r1c2, r1c8, r5c8 form a remote triple due to weakly linked 9s (r1c2 - r3c23 = r3c5 - r7c5 = r7c8 - r5c8)

r1c2, r1c8, r5c8 are three cells containing three digits. They would form a remote triple if it was demonstrated that no digit can be there twice. You give a proof for the 9s (derived weak link 9r1c2 - 9r5c8) To me, a derived weak link between 1r1c2, 1r5c8 should also been exhibited. I found none.
Moreover, the solution of the puzzle contains 1r1c2 AND 1r5c8:

Code: Select all

 +-----------------+-----------------+-----------------+
 |  6    1    2    |  9    3    8    |  4    5    7    |
 |  4    8    7    |  1    5    2    |  9    6    3    |
 |  3    9    5    |  6    7    4    |  8    2    1    |
 +-----------------+-----------------+-----------------+
 |  5    6    9    |  4    1    7    |  3    8    2    |
 |  2    4    8    |  3    6    5    |  7    1    9    |
 |  7    3    1    |  2    8    9    |  6    4    5    |
 +-----------------+-----------------+-----------------+
 |  8    2    4    |  5    9    3    |  1    7    6    |
 |  9    7    6    |  8    2    1    |  5    3    4    |
 |  1    5    3    |  7    4    6    |  2    9    8    |
 +-----------------+-----------------+-----------------+

[Leren]

Code: Select all

*------------------------------------------------*
| 6 c159dH 1259  | 2389 389  289 | 4     b15B 7  |
| 4  8     27    | 1    5    27  | 9      6   3  |
| 3  1579G 1579G | 6    79F  4   |a8-5aA  2   18 |
|----------------+---------------+---------------|
| 5  6     149   | 479  1479 79  | 3      8   2  |
| 2  34    8     | 34   6    5   | 7      19C 19 |
| 7  139   139   | 2389 1389 289 | 6      4   5  |
|----------------+---------------+---------------|
| 8  2     47    | 5    479E 3   | 1      79D 6  |
| 9  57c   6     | 78   2    1   | 58b    3   4  |
| 1  3457  3457  | 4789 4789 6   | 2      579 89 |
*------------------------------------------------*

Kraken Cell r1c2:

5 r3c7 - (5=1) r1c8                                           - 1 r1c2;

5 r3c7 - r8c7 = r8c2                                          - 5 r1c2;

5 r3c7 - (5=1) r1c8 - (1=9) r5c8 - r7c8 = r7c5 - r3c5 = r3c23 - 9 r1c2; => - 5 r3c7; stte

[shye]

Hi shye,
I'm in a trouble with your assertion

r1c2, r1c8, r5c8 form a remote triple due to weakly linked 9s (r1c2 - r3c23 = r3c5 - r7c5 = r7c8 - r5c8)

r1c2, r1c8, r5c8 are three cells containing three digits. They would form a remote triple if it was demonstrated that no digit can be there twice. You give a proof for the 9s (derived weak link 9r1c2 - 9r5c8) To me, a derived weak link between 1r1c2, 1r5c8 should also been exhibited. I found none.
Moreover, the solution of the puzzle contains 1r1c2 AND 1r5c8

oh thank you for pointing that out, thats my bad, i forgot to prove it true for 1s as well
at the very least the deduction still works when accounting for the possibility of double 1 (it would make r1c8 a 5), but it definitely takes away from the elegance...

[Cenoman]

[...]at the very least the deduction still works when accounting for the possibility of double 1 (it would make r1c8 a 5), but it definitely takes away from the elegance...

My concern was your use of the "remote triple" pattern.
My definition of a remote triple: a set of three cells (in at least two sectors), forced to contain one instance of each digit in a set of three. There is no remote triple here. Or am I wrong ?
I missed time to search a fix yesterday. The main finding in your solution is the finned X-Wing 5@r19. Very nice !
No need to put forward the triplet of cells r1c28, r5c8. The ALS r1c28 is enough to prove (9=5)r1c28, so that you can write the derived strong link: FXW(5)r19\c238 = (9)r1c2 and conclude with the AIC:
FXW(5)r19\c238 = (9)r1c2 - r3c23 = r3c5 - r7c5 = r7c8 - (9=85)b9p49 => -5 r8c2
Note that the 1s play no role in that (except the role of ALS-bystanders)

Keep on posting your nice puzzles and nice solutions !

[shye]

yes it would no longer be called a remote triple, instead some form of complex chain

maybe re-writing it like so is simpler:
5r1c2 = [(1=9)r1c2 - 9r3c23 = 9r3c5 - 9r7c5 = 9r7c8 - (9=1)r5c8] - (1=5)r1c8
then with 5r1c2 = 5r1c8 we can use the x-wing

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 6   ef159   1259  | 2389  389   289   | 4    a5-1   7     |
 | 4     8     27    | 1     5     27    | 9     6     3     |
 | 3    g1579 g1579  | 6    h79    4     | 58    2     18    |
 *-------------------+-------------------+-------------------|
 | 5     6     149   | 479   1479  79    | 3     8     2     |
 | 2     34    8     | 34    6     5     | 7    j19    19    |
 | 7     139   139   | 2389  1389  289   | 6     4     5     |
 *-------------------+-------------------+-------------------|
 | 8     2     47    | 5    i479   3     | 1    j79    6     |
 | 9    d57    6     | 78    2     1     |c58    3     4     |
 | 1     3457  3457  | 4789  4789  6     | 2    b579   89    |
 *-----------------------------------------------------------*


[5r1c8 = r9c8 - r8c7 = r8c2 - (5=1*)r1c2] = *9r1c2 - r3c23 = r3c5 - r7c5 = (91)r57c8 => -1 r1c8 ; ste

[SteveG48]

Nice one, Clement.