The New Sudoku Players' Forum

[wapati]

This one has a swordfish but it can be avoided.
There are available: x, xy, xyz, Turbots, sky, sword, UR, that I know of.

Code: Select all

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



[udosuk]

I cannot find a WXYZ wing, could you post a "candidates" picture of it please?

(I am not known for spotting techniques new to myself.) <blush>

After SSTS:

Code: Select all

 *-----------------------------------------------------------*
 | 3     1     9     | 2     4     8     | 7     5     6     |
 | 68    2     78    | 5    *17    16    | 9     4     3     |
 | 4     67    5     |#367   39    69    | 2     8     1     |
 |-------------------+-------------------+-------------------|
 | 5     67    27    | 9     26    3     | 8     1     4     |
 | 68    4     28    | 167   1267  126   | 5     3     9     |
 | 9     3     1     | 8     5     4     | 6     2     7     |
 |-------------------+-------------------+-------------------|
 | 12    8     4     |*16   -126   7     | 3     9     5     |
 | 7     5     3     | 4     89    29    | 1     6     28    |
 | 12    9     6     |*13    38    5     | 4     7     28    |
 *-----------------------------------------------------------*

r7c5=1 => r79c4=[63] & r2c5=7 => no candidate for r3c4
Therefore r7c5<>1

Afterwards, a box-line elimination on r5c4 and a naked pair on c5 will leave you:

Code: Select all

 *--------------------------------------------------*
 | 3    1    9    | 2    4    8    | 7    5    6    |
 | 68   2    78   | 5    17  -16   | 9    4    3    |
 | 4    67   5    |@367  39  -69   | 2    8    1    |
 |----------------+----------------+----------------|
 | 5    67   27   | 9    26   3    | 8    1    4    |
 | 68   4    28   |-67   17  @126  | 5    3    9    |
 | 9    3    1    | 8    5    4    | 6    2    7    |
 |----------------+----------------+----------------|
 | 12   8    4    | 16   26   7    | 3    9    5    |
 | 7    5    3    | 4    89   29   | 1    6    28   |
 | 12   9    6    | 13   38   5    | 4    7    28   |
 *--------------------------------------------------*

Now one or both of the 2 @ cells must be 6, otherwise we'll be left a BUG situation...

Therefore the 3 cells which see both @ cells must not be 6... And the puzzle is solved...

[wapati]

This starts with a finned swordfish and doesn't get much easier after that.
Lots of patterns!

Code: Select all

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


[claudiarabia]

Code: Select all

. . . . 4 . . . .
. 9 . . . . . 2 .
. . 1 8 . 7 3 . .
. . 4 . 1 . 7 . .
6 . . 2 . 8 . . 1
. . 2 . 3 . 8 . .
. . 3 1 . 5 6 . .
. 5 . . . . . 9 .
. . . . 7 . . . .


SE shows a Bi-directional Y-Cycle. But you don't need it. There is an UR Type 1 easy to spot which solves the puzzle. There are also Swordies and all three kinds of wings.

[udosuk]

There is an UR Type 1 easy to spot which solves the puzzle.

The UR type 1 might be easy to spot, but I can't find it...

Managed to find a more advanced UR though...

After SSTS:

Code: Select all

 *-----------------------------------------------------------*
 | 37    23    58    | 359   4     1239  | 19    78    6     |
 | 347   9     58    | 35    6     13    | 14    2     78    |
 | 24    6     1     | 8     29    7     | 3     45    59    |
 |-------------------+-------------------+-------------------|
 | 35    8     4     | 69    1     69    | 7     35    2     |
 | 6     37    79    | 2     5     8     | 49    34    1     |
 | 59    1     2     | 7     3     4     | 8     6     59    |
 |-------------------+-------------------+-------------------|
 | 29    47    3     | 1     29    5     | 6     78    478   |
 | 1     5     67    |-346   8     36    | 2     9    *347   |
 | 8     24    69    |-3469  7     2369  | 5     1    *34    |
 *-----------------------------------------------------------*

There is a UR (type ?) of {34} in r89c49:

r8c4=3 => r8c9=4 (HS r8), r9c4=4 (HS c4/b8), r9c9=3 (HS r9/c9/b9) => deadly pattern
r9c4=3 => r8c4=4 (HS c4/b8), r8c9=3 (HS r8), r9c9=4 (NS) => deadly pattern

(HS=hidden single, NS=naked single)

Therefore r89c4<>3.

And the puzzle is then solved with a box-line interaction followed by a cascade of naked singles...

Any hint on the UR type 1?

[daj95376]

While everyone is looking for the UR_1 in Claudiarabia's puzzle, there is an interesting short Forcing Chain to derive [r2c7]<>1. Five cells with five values in a restricted rectangular arrangement that includes three bivalue cells with two strong links on <1>. Is this just a Forcing Chain and nothing more?

Code: Select all

# [r2c7]=1 => ([r1c7]=9,[r2c6]=3) => ([r1c4]=5,[r2c4]=5) => [r2c7]<>1
 *-----------------------------------------------------------*
 | 37    23    58    |*359   4     1239  |*19    78    6     |
 | 347   9     58    |*35    6    *13    |*14    2     78    |
 | 24    6     1     | 8     29    7     | 3     45    59    |
 |-------------------+-------------------+-------------------|
 | 35    8     4     | 69    1     69    | 7     35    2     |
 | 6     37    79    | 2     5     8     | 49    34    1     |
 | 59    1     2     | 7     3     4     | 8     6     59    |
 |-------------------+-------------------+-------------------|
 | 29    47    3     | 1     29    5     | 6     78    478   |
 | 1     5     67    | 346   8     36    | 2     9     347   |
 | 8     24    69    | 3469  7     2369  | 5     1     34    |
 *-----------------------------------------------------------*


[ronk]

Is this just a Forcing Chain and nothing more?

You can apply the ALS xz-rule:

Code: Select all

Sets A = {r1c7} = {19}
     B = {r12c4,r2c6} = {1359}
     x = 9
     z = 1

At least one of the sets cannot ultimately contain the digit 9. Therefore at least one of the sets must contain the digit 1. Any 1s candidates that see all the 1s in both sets may be eliminated.

Some consider it a generalized wxyz-wing.

[daj95376]

Well, I guess it doesn't qualify for the New Multi-Spoke Pattern. No big surprise.

[claudiarabia]

There is an UR Type 1 easy to spot which solves the puzzle.

The UR type 1 might be easy to spot, but I can't find it...

Any hint on the UR type 1?

You can see the UR type 1 also running the puzzle through the SE. When SE shows the bi-directional y-cycle you can see the Rectangle. I had my own special way through this puzzle. For instance just after placing some singles you may spot also an xy-wing. SE makes some pointing coming to the same elimination. Here is my way.

The grid shows the situation before Step 11 (UR Type 1) is made.

Code: Select all


 *-----------------------------------------------------------*
 | 2357  23    58    | 359   4     1239  | 19    78    6     |
 | 347   9     58    | 35    6     13    | 14    2     78    |
 | 24    6     1     | 8     29    7     | 3     45    59    |
 |-------------------+-------------------+-------------------|
 | 359   8     4     | 69    1     69    | 7     35    2     |
 | 6     37    79    | 2     5     8     | 49    34    1     |
 | 59    1     2     | 7     3     4     | 8     6     59    |
 |-------------------+-------------------+-------------------|
 | 29    47    3     | 1     29    5     | 6     78    478   |
 | 1     5     67    | 346   8     36    | 2     9     347   |
 | 8     24    69    | 3469  7     2369  | 5     1     34    |
 *-----------------------------------------------------------*


I had made the following Steps

After the usual pointing, claiming, setting singles:

1.swordfish in r367 c158 upon the 9
2.swordfish in r346 c189 upon the 5 -->r9c7=5
3.xy-wing eliminating 6 in r12c6 (wing-cells r5c5, r4c6, r2c5)
4.naked triplet in r125c8 consisting of 149
5.hidden pair in r36c9 consisting of 59
6.Skycraper in r3c15/c6r19 upon 2 eliminating 2 in r9c1 => r9c1 =8
7.naked triplet in r589c3 consisting of 679
8.skyscraper in r2c19/c8r17 upon 7 eliminating 7 in r7c1
9.naked pair in r7c15 consisting of 29
10.X-wing upon 2 in r19c25 eliminating 2 in r1c1
11.UR type 1 in r37c15 upon 29 eliminating 2 in r3c1

Then the puzzle is solved.

[re'born]

The grid shows the situation before Step 11 (UR Type 1) is made.

Code: Select all


 *-----------------------------------------------------------*
 | 2357  23    58    | 359   4     1239  | 19    78    6     |
 | 347   9     58    | 35    6     13    | 14    2     78    |
 | 24    6     1     | 8     29    7     | 3     45    59    |
 |-------------------+-------------------+-------------------|
 | 359   8     4     | 69    1     69    | 7     35    2     |
 | 6     37    79    | 2     5     8     | 49    34    1     |
 | 59    1     2     | 7     3     4     | 8     6     59    |
 |-------------------+-------------------+-------------------|
 | 29    47    3     | 1     29    5     | 6     78    478   |
 | 1     5     67    | 346   8     36    | 2     9     347   |
 | 8     24    69    | 3469  7     2369  | 5     1     34    |
 *-----------------------------------------------------------*


I had made the following Steps

After the usual pointing, claiming, setting singles:
.
.
.
11.UR type 1 in r37c15 upon 29 eliminating 2 in r3c1

Then the puzzle is solved.

Your UR type 1 spans 4 boxes and is therefore an invalid move. It happens to me all the time.

[claudiarabia]

The grid shows the situation before Step 11 (UR Type 1) is made.

Code: Select all


 *-----------------------------------------------------------*
 | 2357  23    58    | 359   4     1239  | 19    78    6     |
 | 347   9     58    | 35    6     13    | 14    2     78    |
 | 24    6     1     | 8     29    7     | 3     45    59    |
 |-------------------+-------------------+-------------------|
 | 359   8     4     | 69    1     69    | 7     35    2     |
 | 6     37    79    | 2     5     8     | 49    34    1     |
 | 59    1     2     | 7     3     4     | 8     6     59    |
 |-------------------+-------------------+-------------------|
 | 29    47    3     | 1     29    5     | 6     78    478   |
 | 1     5     67    | 346   8     36    | 2     9     347   |
 | 8     24    69    | 3469  7     2369  | 5     1     34    |
 *-----------------------------------------------------------*


I had made the following Steps

After the usual pointing, claiming, setting singles:
.
.
.
11.UR type 1 in r37c15 upon 29 eliminating 2 in r3c1

Then the puzzle is solved.

Your UR type 1 spans 4 boxes and is therefore an invalid move. It happens to me all the time.

So it is like the thing of the Unique Loop ravel explained here
http://forum.enjoysudoku.com/viewtopic.php?t=5009&postdays=0&postorder=asc&start=270
But it workes. Remembers me of the Math-problems with the brackets. If there is one pair of brackets with a minus inside and you forget to change the minus then, you made a mistake, but are there two pairs of brackets in one problem, two minuses are making one plus and you didn't make a mistake in the End when you forget to switch from minus into plus.

So I'm really grateful to you that you caught this false Unique Rectangle in the act finally before I'm going to mess some puzzles. Now I have to study the wicked bi-directional y-cycle.

[re'born]

Remembers me of the Math-problems with the brackets. If there is one pair of brackets with a minus inside and you forget to change the minus then, you made a mistake, but are there two pairs of brackets in one problem, two minuses are making one plus and you didn't make a mistake in the End when you forget to switch from minus into plus.

Johannes Kepler is famous for doing that in his work. I guess in math, two wrongs can make a right.

So I'm really grateful to you that you caught this false Unique Rectangle in the act finally before messing some puzzles. Now I have to study the wicked bi-directional y-cycle.

I'll stick with udosuk's solution.

[udosuk]

I'll still with udosuk's solution.

Thanks... But personally I think the ALS-xz/generalized WXYZ-wing found by Danny & explained by Ron is a better solution... Whenever I've got a choice non-uniqueness moves are usually better...

I remember last time someone has explained the type of that UR I found, but I still can't locate the source... Could any kind soul give me a link? Thanks!

[claudiarabia]

I remember last time someone has explained the type of that UR I found, but I still can't locate the source... Could any kind soul give me a link? Thanks!

Do you mean Mike Barkers postings on these pages?
http://forum.enjoysudoku.com/viewtopic.php?t=4899&start=15
http://forum.enjoysudoku.com/viewtopic.php?p=26448#p26448

[re'born]

I'll still with udosuk's solution.

Thanks... But personally I think the ALS-xz/generalized WXYZ-wing found by Danny & explained by Ron is a better solution... Whenever I've got a choice non-uniqueness moves are usually better...

The reason I prefer your move is that most uniqueness based moves are easy to spot. ALS xz-moves, I don't have a clue where to begin looking. Your move, I will catch nearly every time. By the way, as far as preferring non-uniqueness moves goes, don't forget RW's overlooked article Logical use of uniqueness technique in an uniqueness test.