The New Sudoku Players' Forum

[daj95376]

I'm going to use this thread for puzzles and PMs that I find interesting. Today, I discovered an XY-Ring while manually examining a continuous loop XY-Chain. Did I catch all of the eliminations?

Code: Select all

.52..7..49..5...1.7.834..95.95.....2..1.7....3....4.........5...73.....95.92...41

 +--------------------------------------------------------------+
 | *16    5     2     |  18-6  9     7     |  3    *68    4     |
 |  9     3     4     |  5     26    268   |  268   1     7     |
 |  7    *16    8     |  3     4     126   |  26    9     5     |
 |--------------------+--------------------+--------------------|
 |  468   9     5     |  168   1368  1368  |  14    7     2     |
 |  2468  24-6  1     |  689   7     25    |  49    35    36    |
 |  3    *26    7     |  19   *25    4     |  19   *58    68    |
 |--------------------+--------------------+--------------------|
 |  124   124   6     |  7     18    9     |  5     23-8  38    |
 |  12    7     3     |  4     158   158   |  68    26-8  9     |
 |  5     8     9     |  2     36    36    |  7     4     1     |
 +--------------------------------------------------------------+


Note: Sudopedia has an empty entry for XY-Ring. Jeff indicates that it has four cells/nodes/vertices/whatever. However, Google lists other Sudoku sites for XY-Ring where it's defined as a continuous loop XY-Chain of any length.

[hobiwan]

I think you covered everything. My solver finds additional eliminations via XY-Chains, but none that can be incorporated into your loop.

[daj95376]

Thanks hobiwan for checking my results!

[daj95376]

This puzzle made it from an AU site to Eureka! recently. Unfortunately, I didn't find ttt's solution for comparison. No matter because he probably did something elegant.

Code: Select all

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


Code: Select all

# after basic SSTS -- excluding colors and multiple colors
 *--------------------------------------------------------------------*
 | 358    346    368    | 348    2      1      | 45678  9      4578   |
 | 389    7      368    | 3489   36     5      | 468    2      1      |
 | 2589   1246   1268   | 489    67     4678   | 3      456    458    |
 |----------------------+----------------------+----------------------|
 | 6      12     1259   | 1245   157    47     | 14579  8      3      |
 | 4      123    1235   | 12358  9      78     | 157    157    6      |
 | 7      8      1359   | 1345   1356   46     | 1459   145    2      |
 |----------------------+----------------------+----------------------|
 | 238    236    7      | 15     15     239    | 2468   46     489    |
 | 1      5      268    | 7      4      29     | 268    3      89     |
 | 23     9      4      | 6      8      23     | 157    157    57     |
 *--------------------------------------------------------------------*

  finned X-Wing  r18\c37           =>  [r23c3]<>6

  8r7c7 8r8c3 6r8c7 2r7c7          =>  [r7c7]<>8   (chain)

  3r7c2 3r56c3 8r2c3 6r1c3 [b7]~2  =>  [r7c2]<>3   (SIN)

# SSTS


Q: After the SIN elimination, there's (23) UR Type 4 [r79c16] that's not necessary. Are there any URs present after the finned X-Wing?

[Edit: inserted SIN as proper term]

[wintder]

Early on there is a hidden UR. It doesn't help me any, does it help you?

Code: Select all

.---------------------.---------------------.---------------------.
| 358    346    368   | 348    2      1     | 45678  9      4578  |
| 389    7      368   | 3489   36     5     | 468    2      1     |
| 2589   1246   1268  | 489    67     4678  | 3      456    458   |
:---------------------+---------------------+---------------------:
| 6      12     1259  | 1245   157    47    | 14579  8      3     |
| 4      123    1235  | 12358  9      78    | 157    157    6     |
| 7      8      1359  | 1345   1356   46    | 1459   145    2     |
:---------------------+---------------------+---------------------:
|*38-2   236    7     | 15     15    *239   | 2468   46     489   |
| 1      5      268   | 7      4      29    | 268    3      89    |
|*23     9      4     | 6      8     *23    | 157    157    57    |
'---------------------'---------------------'---------------------'

[daj95376]

Early on there is a hidden UR. It doesn't help me any, does it help you?

wintder: Thanks for the reply. Unfortunately, I'm not up on hidden URs. And, I agree with your assessment that it doesn't seem to help.

I keep thinking there must be a (15) UR in this mess -- especially with (157) locked into [r59c78] and [r9c9]=57.

[Steve K]

daj, ttt's solution is among the comments on the "tough" page for that date: http://sudoku.com.au/1V21-7-2008-sudoku.aspx
(columns are letters, rows are numbers, bottom left corner cell is a1)

[daj95376]

Steve K: Thanks for the link. Unfortunately, I only understand the rudamentary basics of Eureka notation. ttt's solution eludes me.

[daj95376]

[Withdrawn: discovered that I was describing a SIN.]

[daj95376]

I keep tweaking my puzzle generator hoping it will generate puzzles that are difficult enough to be interesting. Maybe this one qualifies. It can be solved with SSTS, fish, and chains. No forcing nets needed ... just patience.

Code: Select all

 +-----------------------+
 | . . 4 | . 5 8 | . . . |
 | . . 7 | 6 . . | . . . |
 | 5 2 3 | . . . | . . . |
 |-------+-------+-------|
 | . 3 . | 1 7 . | 8 6 . |
 | 4 . . | 8 . . | 5 3 . |
 | 6 . . | . . 3 | . . 7 |
 |-------+-------+-------|
 | . . . | 3 6 . | 4 . . |
 | . . . | 4 8 . | . 9 . |
 | . . . | . . 9 | . . 3 |
 +-----------------------+   # P_Set_F: #21


[ttt]

Hi All,
Nice puzzle from sudoku.com.au (tough page Aug. 1st/08), ER 8.8 but can solve by AIC’s only.

Code: Select all

 *-----------*
 |..8|7..|..5|
 |...|...|9..|
 |9..|6..|.4.|
 |---+---+---|
 |...|.4.|.6.|
 |.35|...|41.|
 |.7.|.2.|...|
 |---+---+---|
 |.9.|..5|..8|
 |..3|...|...|
 |6..|..1|2..|
 *-----------*

After SSTS
 *-----------------------------------------------------------------------------*
 | 123     1246    8       | 7       139     249     | 136     23      5       |
 | 12357   12456   1247    | 2348    1358    248     | 9       2378    1367    |
 | 9       125     127     | 6       1358    28      | 1378    4       137     |
 |-------------------------+-------------------------+-------------------------|
 | 128     128     9       | 5       4       378     | 378     6       237     |
 | 28      3       5       | 89      6789    6789    | 4       1       279     |
 | 4       7       6       | 1       2       389     | 358     3589    39      |
 |-------------------------+-------------------------+-------------------------|
 | 127     9       1247    | 234     367     5       | 1367    37      8       |
 | 12578   12458   3       | 2489    6789    246789  | 1567    579     14679   |
 | 6       458     47      | 3489    3789    1       | 2       3579    3479    |
 *-----------------------------------------------------------------------------*

Good luck… !

PS. sorry Daj, I post puzzle here...

[daj95376]

Hello ttt. Welcome to my ramble.

Well, your puzzle has my solver stumped. After five unproductive chains, it was forced to go to a forcing net (that was present w/o the chains). I'm looking forward to your solution.

[ttt]

Hi daj,
Thanks!
First, I apologize I have to present my solution by Eureka (or AIC) notation. I can’t present by NL notation at present, sorry again about that (I’m afraid, ronk would require me to remind him something… )

1) (3=7)r7c8-(7)r7c1=(hp57)r28c1-(3)r2c1=(3)r1c1 => r1c8<>3, single r1c8=2
2) (1)r23c3=(1)r7c3-(hp24)r7c34=(2)r7c1-(hp28)r45c1=(1)r4c1 => r12c1<>1, single r1c1=3
3) (1)r8c9=(1)r23c9-(1=6)r1c7-(6)r2c9=(6)r8c9 => r8c9<>479, r3c7<>1, some singles
4) 8’s : r3c7=r2c8-r6c8=r6c6 => r3c6<>8, some singles
5) XY-wing : r5c1=82, r5c9=27, r4c8=78 => r4c1<>8, singles to the end

I found some chains more but not necessary for solution then I deducted on my solution.

Thanks again,
ttt

[daj95376]

ttt: An impressive solution using subsets to generate some eliminations.

Since my solver doesn't incorporate subsets in chains, it solved the original puzzle with ...

1) SSTS
2) SIN: 4r8c9 6r2c9 1r3c9 3r1c7 3r3c5 5r2c5 1r1c5 [r1]~2 => [r8c9]<>4
3) SSTS

[ttt]

Hi daj,
I present your elimination r8c9=4 by using dual Kraken - 3's on row 3 and cell r1c7 :

Code: Select all

(3)r3c5-(hp15)r23c5=(1)r1c5-(ht123)r1c178=(6)r1c7-(6)r2c9=(6)r8c9
 ||
(3)r3c79-(3)r1c7
          ||
         (1)r1c7-(1)r23c9=(1)r8c9
          ||
         (6)r1c7-(6)r2c9=(6)r8c9

=> r8c9<>4

ttt