The New Sudoku Players' Forum

[richardm]

Did you notice that the Time last Friday (18th May) had a wxyz-wing?
The original puzzle was this:

Code: Select all

59. .14 ...
... .3. ...
.32 8.. .5.

..5 6.. ..2
.6. ... .3.
7.. ..3 5..

.1. ..7 49.
... .9. ...
... 32. .76

I thought the trick in r3/4 c5/6 was quite neat.

Richard

[udosuk]

Here is a textbook solution of this puzzle:

Code: Select all

59..14...
....3....
.328...5.
..56....2
.6.....3.
7....35..
.1...749.
....9....
...32..76

Naked single: r7c4=5
Hidden singles: r4c1=3, r8c4=4, r8c9=5, r6c8=6
Locked candidates: 1 of c6 locked in r89c6, 1 of b6 locked in r4c78, 1 of b3 locked in r23c9
Hidden pair/naked triple: r3c19={14}
X-wings: 7 of c57 locked in r34c57, 9 of c67 locked in r34c67

The rest are all naked singles.

I can't find any WXYZ-wing necessary.

[richardm]

Evidently there's more than one way to skin this cat.

I thought the four adjancet cells each with a pair of from 6,7,8,9 quite neat. I did use one x-wing of 4's

Richard

[udosuk]

I thought the four adjancet cells each with a pair of from 6,7,8,9 quite neat. I did use one x-wing of 4's

In that case you've quoted the wrong technique. The move is in fact an XY-ring (aka continuous XY-chain). See the following links for more explanations and examples:

http://forum.enjoysudoku.com/viewtopic.php?t=2966
http://forum.enjoysudoku.com/viewtopic.php?t=5419

The fastest way to get to that move is as following:

Naked singles: r7c4=5
Hidden singles: r7c1=2, r6c2=2, r8c4=4, r9c2=5, r6c8=6
Locked candidates: 1 of c6 locked in r89c6
X-wing: 4 of r24 locked in r24c28

Now we get to the following position:

Code: Select all

 *-----------------------------------------------------------------------------*
 | 5       9       678     | 27      1       4       | 23678   28      378     |
 | 168     478     1678    | 279     3      -6-925   | 126789  1248    1789    |
 |-614     3       2       | 8      *67     *69      |-6179    5       1479    |
 |-------------------------+-------------------------+-------------------------|
 |-8139   -84      5       | 6      *78     *89      |-8179   -814     2       |
 | 1489    6       1489    | 1279   -7458   -9258    | 1789    3       14789   |
 | 7       2       1489    | 19     -84      3       | 5       6       1489    |
 |-------------------------+-------------------------+-------------------------|
 | 2       1       368     | 5       68      7       | 4       9       38      |
 | 368     78      3678    | 4       9       168     | 1238    128     1358    |
 | 489     5       489     | 3       2       18      | 18      7       6       |
 *-----------------------------------------------------------------------------*

So r2c6+r3c17<>6, r4c1278+r6c5<>8, r5c5<>7, r25c6<>9

[richardm]

Thanks for the links. I didn't know that was what they were called.
Richard

[udosuk]

richardm's xy-ring in fact produces 13 eliminations. I missed 2 last time:

Code: Select all

 *-----------------------------------------------------------------------------*
 | 5       9       678     | 27      1       4       | 23678   28      378     |
 | 168     478     1678    | 279     3      -6-925   | 126789  1248    1789    |
 |-614     3       2       | 8      *67     *69      |-6179    5       1479    |
 |-------------------------+-------------------------+-------------------------|
 |-8139   -84      5       | 6      *78     *89      |-8179   -814     2       |
 | 1489    6       1489    | 1279   -7-845  -8-925   | 1789    3       14789   |
 | 7       2       1489    | 19     -84      3       | 5       6       1489    |
 |-------------------------+-------------------------+-------------------------|
 | 2       1       368     | 5       68      7       | 4       9       38      |
 | 368     78      3678    | 4       9       168     | 1238    128     1358    |
 | 489     5       489     | 3       2       18      | 18      7       6       |
 *-----------------------------------------------------------------------------*

So r2c6+r3c17<>6, r4c1278+r5c56+r6c5<>8, r5c5<>7, r25c6<>9

After that and a few naked singles:

Code: Select all

 *-----------------------------------------------------------------------------*
 | 5       9       678     | 27      1       4       | 23678   28      378     |
 | 168     78      1678    | 279     3       5       | 126789  248     1789    |
 | 14      3       2       | 8       67      69      | 179     5       1479    |
 |-------------------------+-------------------------+-------------------------|
 | 39      4       5       | 6       78      89      | 79      1       2       |
 | 189     6       189     | 179     5       2       | 789     3       4789    |
 | 7       2       189     | 19      4       3       | 5       6       89      |
 |-------------------------+-------------------------+-------------------------|
 | 2       1       368     | 5       68      7       | 4       9       38      |
 | 368     78      3678    | 4       9       168     | 1238    28      1358    |
 | 489     5       489     | 3       2       18      | 18      7       6       |
 *-----------------------------------------------------------------------------*

Then the following moves solve it:

Hidden singles: r5c9=4, r8c9=5
Locked candidates: 1 of c7 locked in r89c7, 7 of c7 locked in r45c7

The rest are all naked singles.

[Pat]

#1335 -- Super Fiendish

[ 26 clues ]

Code: Select all

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



my solution-path used:
one X-wing (fish of order 2)
and 3 box-line interactions (fish of order 1)

1. 4 c28\r24
   
2. 8 b5\r4
   
3. 1 b9\c7
   7 b6\c7

[richardm]

Pat, I am slightly puzzled by your moves (aka, I don't understand the notation). Can you explain?

richardm

[udosuk]

Pat has omitted all the singles moves. Here is a log that includes all the singles moves required for the 4 moves shown by Pat:

Code: Select all

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

Naked single: r7c4=5 => r2c6=r5c5=r8c9=r9c2=5
Hidden single (c6): r5c6=2
Hidden single (b4): r6c2=2
Hidden single (r7): r7c1=2
Hidden single (b6): r6c8=6
Hidden single (b8): r8c4=4
1. X-wing of 4 in r24c28: r2c139<>4, r4c15<>4
Hidden single (b5): r6c5=4
2. Box-line interaction (b5,r4): 8 locked in r4c56 => r4c1278<>8
Naked single: r4c2=4 => r2c8=r3c1=r5c9=r9c3=4
Naked single: r4c8=1
3a. Box-line interaction (b9,c7): 1 locked in r89c7 => r23c7<>1
3b. Box-line interaction (b6,c7): 7 locked in r45c7 => r123c7<>7
Hidden single (r3): r3c9=1
Hidden single (r3): r3c5=7

The rest are all naked singles.

[Pat]

thanks, udosuk! once again it turns out that my explanation was not as clear as i may have imagined --

[richardm]

yes, that makes more sense. very straight forward, once again no need for any fancy techniques.
thanks,