## Need Help With Hard Puzzle

Post the puzzle or solving technique that's causing you trouble and someone will help

### Need Help With Hard Puzzle

I don't fully understand the "X-Wing" and "Swordfish" techniques. That may be the reason I'm stumped on this puzzle. Any help or hints would be greatly appreciated.

(X,X,X) (8,5,X) (1,6,9)
(9,5,1) (6,3,7) (8,4,2)
(X,X,8) (1,X,9) (7,3,5)

(X,9,X) (5,X,X) (4,1,X)
(8,1,X) (9,X,X) (X,5,6)
(X,X,5) (X,X,1) (X,9,X)

(5,4,6) (X,X,X) (9,2,1)
(1,7,3) (2,9,6) (5,8,4)
(2,8,9) (4,1,5) (6,7,3)

Thanks
turnthepage

Posts: 8
Joined: 04 May 2006

Code: Select all

*--------------------------------------------------------------------*
| 347    23     247    | 8      5      24     | 1      6      9      |
| 9      5      1      | 6      3      7      | 8      4      2      |
| 46     26     8      | 1      24     9      | 7      3      5      |
|----------------------+----------------------+----------------------|
| 367    9      27     | 5      2678   238    | 4      1      78     |
| 8      1      247    | 9      247    234    | 23     5      6      |
| 3467   236    5      | 37     24678  1      | 23     9      78     |
|----------------------+----------------------+----------------------|
| 5      4      6      | 37     78     38     | 9      2      1      |
| 1      7      3      | 2      9      6      | 5      8      4      |
| 2      8      9      | 4      1      5      | 6      7      3      |
*--------------------------------------------------------------------*

This is not a trivial puzzle. I ran it through Simple Sudoku, and it used an X Wing and then 2 XY Wings before getting stuck. A 9 cell XY chain then solved it. There is probably a shorter chain, but that's the first one I saw.

First things first, though. There is an X Wing on 4s in rows 3 and 6. The 4s in those rows are restricted to the same columns. All other 4s in those columns can be excluded.

The X Wing is the simplest step on the board right now. Try to see it.
Sped

Posts: 126
Joined: 26 March 2006

Sped, I found the x wing and the 2 xy wings but am now stuck. If no one jumps in, I'll post where I'm at later.
Hud

Posts: 570
Joined: 29 October 2005

Hud wrote:Sped, I found the x wing and the 2 xy wings but am now stuck. If no one jumps in, I'll post where I'm at later.

After the X Wing and a couple of XY Wings, here's where Simple Sudoku gets stuck:

Code: Select all
*--------------------------------------------------*
| 37   23   47   | 8    5    24   | 1    6    9    |
| 9    5    1    | 6    3    7    | 8    4    2    |
| 46   26   8    | 1    24   9    | 7    3    5    |
|----------------+----------------+----------------|
| 36   9    2    | 5    68   38   | 4    1    7    |
| 8    1    47   | 9    27   24   | 3    5    6    |
| 47   36   5    | 37   467  1    | 2    9    8    |
|----------------+----------------+----------------|
| 5    4    6    | 37   78   38   | 9    2    1    |
| 1    7    3    | 2    9    6    | 5    8    4    |
| 2    8    9    | 4    1    5    | 6    7    3    |
*--------------------------------------------------*

I found a shorter XY chain :

7-(r6c4)-3-(r4c6)-8-(r4c5)-6-(r4c1)-3-(r1c1)-7

which eliminates the 7 in r6c1, solving the puzzle.

In nice loop notation:

[r6c1]-7-[r6c4]-3-[r4c6]-8-[r4c5]-6-[r4c1]-3-[r1c1]-7-[r6c1], => r6c1<>7
Sped

Posts: 126
Joined: 26 March 2006

Sped, that's my grid exactly. I'm horrible at colouring and chains, but will look at it while watching "Survivor".
Hud

Posts: 570
Joined: 29 October 2005

Hi Guys,

Code: Select all
*--------------------------------------------------*
| 37   23   47   | 8    5    24   | 1    6    9    |
| 9    5    1    | 6    3    7    | 8    4    2    |
| 46   26   8    | 1    24   9    | 7    3    5    |
|----------------+----------------+----------------|
| 36   9    2    | 5    68   38   | 4    1    7    |
| 8    1    47   | 9    27   24   | 3    5    6    |
| 47   36   5    | 37   46+7 1    | 2    9    8    |
|----------------+----------------+----------------|
| 5    4    6    | 37   78   38   | 9    2    1    |
| 1    7    3    | 2    9    6    | 5    8    4    |
| 2    8    9    | 4    1    5    | 6    7    3    |
*--------------------------------------------------*

This is a BUG+1 grid allowing you to set r6c5 = 7. From here the puzzle solves with singles.
re'born

Posts: 551
Joined: 31 May 2007

Here are three possibilities after the X-wing and the XY-wings: an Almost Locked Set, a 4-node XY-chain, and a 4-node Nice Loop.

Code: Select all
+-------------+--------------+----------+
|  37  23  47 |   8    5  24 |  1  6  9 |
|   9   5   1 |   6    3   7 |  8  4  2 |
| *46 -26   8 |   1   24   9 |  7  3  5 |
+-------------+--------------+----------+
| -36   9   2 |   5   68  38 |  4  1  7 |
|   8   1  47 |   9   27  24 |  3  5  6 |
| #47 #36   5 | #37  467   1 |  2  9  8 |
+-------------+--------------+----------+
|   5   4   6 |  37   78  38 |  9  2  1 |
|   1   7   3 |   2    9   6 |  5  8  4 |
|   2   8   9 |   4    1   5 |  6  7  3 |
+-------------+--------------+----------+

ALS xz-rule with A=1 cells: r3c1-4-r6c124 => r3c2<>6,r4c1<>6

Code: Select all
+-------------+--------------+----------+
|  37  23  47 |   8    5  24 |  1  6  9 |
|   9   5   1 |   6    3   7 |  8  4  2 |
| *46  26   8 |   1   24   9 |  7  3  5 |
+-------------+--------------+----------+
| *36   9   2 |   5   68 -38 |  4  1  7 |
|   8   1  47 |   9   27  24 |  3  5  6 |
| *47 -36   5 | *37  467   1 |  2  9  8 |
+-------------+--------------+----------+
|   5   4   6 |  37   78  38 |  9  2  1 |
|   1   7   3 |   2    9   6 |  5  8  4 |
|   2   8   9 |   4    1   5 |  6  7  3 |
+-------------+--------------+----------+

4-node XY-chain: r346c1|r6c4 => r6c2<>3,r4c6<>3

Code: Select all
+-------------+--------------+----------+
|  37  23  47 |   8    5  24 |  1  6  9 |
|   9   5   1 |   6    3   7 |  8  4  2 |
|  46 -26   8 |   1  *24   9 |  7  3  5 |
+-------------+--------------+----------+
|  36   9   2 |   5   68  38 |  4  1  7 |
|   8   1  47 |   9   27  24 |  3  5  6 |
|  47 *36   5 |  37 *467   1 |  2  9  8 |
+-------------+--------------+----------+
|   5   4   6 |  37   78  38 |  9  2  1 |
|   1   7   3 |   2    9   6 |  5  8  4 |
|   2   8   9 |   4    1   5 |  6  7  3 |
+-------------+--------------+----------+

Nice Loop: r3c2=2=r3c5=4=r6c5=6=r6c2~6~r3c2 => r3c2<>6
Mike Barker

Posts: 458
Joined: 22 January 2006

rep'nA wrote:Hi Guys,

Code: Select all
*--------------------------------------------------*
| 37   23   47   | 8    5    24   | 1    6    9    |
| 9    5    1    | 6    3    7    | 8    4    2    |
| 46   26   8    | 1    24   9    | 7    3    5    |
|----------------+----------------+----------------|
| 36   9    2    | 5    68   38   | 4    1    7    |
| 8    1    47   | 9    27   24   | 3    5    6    |
| 47   36   5    | 37   46+7 1    | 2    9    8    |
|----------------+----------------+----------------|
| 5    4    6    | 37   78   38   | 9    2    1    |
| 1    7    3    | 2    9    6    | 5    8    4    |
| 2    8    9    | 4    1    5    | 6    7    3    |
*--------------------------------------------------*

This is a BUG+1 grid allowing you to set r6c5 = 7. From here the puzzle solves with singles.

I've never looked at BUG before. Tell me if I have this right..

A BUG grid, one with all bivalue cells, and in which all candidates that appear in a group do so exactly twice, can have either zero or more than one solution, but not one solution. So a BUG grid is invalid.

In this grid, excluding 7 from r6c5 would make it a BUG, so 7 cannot be excluded from that cell. r6c5 must be 7.

Do I have that right?

How often do these BUGs come up?
Sped

Posts: 126
Joined: 26 March 2006

### Re: Need Help With Hard Puzzle

turnthepage wrote:"I don't fully understand the "X-Wing" and "Swordfish" techniques. .."

If case you need further help to understand the "X-wing" technique note that candidate 4 appears twice in row3 (r3) and also twice in r6. You'll also notice this same candidate occupies the same two columns (c1 and c5).

This leaves you two options:
(a) either the 4 goes in r3c1 which then places the other 4 in r6c5 or
(b) the 4 goes in r3c5 which then places the other 4 in r6c1.

You still don't know which of these two options is correct but what you can now deduce is that any other candidate 4's in either of the two columns1 and 5 can be excluded - so exclude the 4's from r1c1 and r5c5.

Remember that the "X-wing" technique requires the particular candidate to appear twice and only twice either in two rows and sharing the same two columns in which case the eventual exclusions occur in columns or, using the same logic, where the particular candidate appears twice and only twice in two columns and sharing the same two rows then the exclusions occur in rows.

If you click on HERE you can read up more details about the concepts of both the "X-wing" and "Swordfish" techniques.

Cec
Cec

Posts: 1039
Joined: 16 June 2005

### XY-Wing

Can someone explain the XY-Wing to me? I looked it up on the internet but I still don't understand it.

Thanks!!!
turnthepage

Posts: 8
Joined: 04 May 2006

In an XYwing you have 2 cells that share a group (row, cell or box) and also share one candidate (XY, XZ).
If one of those cells is in another group with the unshared candidates (YZ) then you can eliminate Z from cells that see both XZ & YZ cells.

Code: Select all

3     4     19     | 6     5     8      | 2     7     19
89   *18    5      | 7     4     2      | *19   6     3
6     2     7      | 1     9     3      | 5     8     4
-------------------+--------------------+-------------------
4    #18    19     | 3     7     5      | *89   2     6
5     6     2      | 8     1     9      | 4     3     7
89    7     3      | 4     2     6      | 189   5     19
-------------------+--------------------+-------------------
7     9     8      | 2     3     4      | 6     1     5
2     3     4      | 5     6     1      | 7     9     8
1     5     6      | 9     8     7      | 3     4     2

XY = r2c7 = 19
XZ = r4c7 = 89
YZ = r2c2 = 18
=> r4c2 <> 8 (sees both 8s)

Code: Select all

3     4     19     | 6     5     8      | 2     7     19
89   #18    5      | 7     4     2      | *19   6     3
6     2     7      | 1     9     3      | 5     8     4
-------------------+--------------------+-------------------
4    *18    19     | 3     7     5      | *89   2     6
5     6     2      | 8     1     9      | 4     3     7
89    7     3      | 4     2     6      | 189   5     19
-------------------+--------------------+-------------------
7     9     8      | 2     3     4      | 6     1     5
2     3     4      | 5     6     1      | 7     9     8
1     5     6      | 9     8     7      | 3     4     2

XY = r4c7 = 89
XZ = r4c2 = 18
YZ = r2c7 = 19
=> r2c2 <> 1 (sees both 1s)
emm

Posts: 987
Joined: 02 July 2005