The New Sudoku Players' Forum

[GregFiore]

I have used X-Wing, Forced Chains, etc and can only solve this puzzle by guessing! This is the original puzzle. What technique solves it? Help
please!

|3--|--8|4--|
|--7|--4|6-8|
|---|-1-|-7-|

|9--|--3|52-|
|--1|---|7--|
|-34|1--|--6|

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

Greg Fiore

[tso]

It can be solved with a couple of short forcing chains.

[fermat]

You didn't mention an xyz wing which is there, with an x wing and two forcing chains. (I can't solve it myself, I used an analyzer.)

[tso]

I didn't see the xyz-wing. Here's my solution:

Here's the state of the puzzle just after finding an x-wing:

Code: Select all

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

Code: Select all

+-------------------+-------------------+-------------------+
| 3     256   569   | 2679  2567  8     | 4     1     259   |
| 1     25    7     | 239   235   4     | 6     359   8     |
| 2458  24568 5689  | 2369  1     259   | 39    7     2359  |
+-------------------+-------------------+-------------------+
| 9     678   68    | 678   4     3     | 5     2     1     |
| 258   2568  1     | 2689  2568  259   | 7     34    34    |
| 257   3     4     | 1     25    257   | 89    89    6     |
+-------------------+-------------------+-------------------+
| 47    1    [58]   |{238}  9     27    |[38]   6     345   |
| 6     47    3     | 5     78    1     | 2     489   49    |
|[58]   9     2     | 4    [38]   6     | 1    {358}  7     |
+-------------------+-------------------+-------------------+

Look at the interesting pattern of cells in [brackets].
At least one of the two [38] cells must be 3, eliminating the
candidate 3 from the two cells in {braces} -- the two cells both
can 'see'. This is a simple xy forcing chain.


After some singles and naked pairs:

Code: Select all

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

Code: Select all

+-------------------+-------------------+-------------------+
| 3     256   69    |{2679}[67]   8     | 4     1     25    |
| 1     25    7     | 39    25    4     | 6     39    8     |
| 245   24568 689   | 2369  1     259   | 39    7     25    |
+-------------------+-------------------+-------------------+
| 9     678   68    | 678   4     3     | 5     2     1     |
| 25    2568  1     | 2689  68    259   | 7     34    34    |
| 257   3     4     | 1     25    257   | 89    89    6     |
+-------------------+-------------------+-------------------+
| 47    1     5     |[28]   9     27    | 38    6     34    |
| 6     47    3     | 5    [78]   1     | 2     48    9     |
| 8     9     2     | 4     3     6     | 1     5     7     |
+-------------------+-------------------+-------------------+

Examine the cells in [brackets].
r1c5=7 -> r8c5=8 -> r7c4=2 -> r1c4<>2
r1c5=6 -> r1c4=7 (only cell left in row and box that can be 7) -> r1c4<>2
Therefore, r1c4<>2. This gives you a [69][679][67] naked triple. After this, there's some more pairs.

[fermat]

I didn't see the xyz-wing. Here's my solution:

It is there, I see, just of no importance. Sorry.

Code: Select all

+-------------------+-------------------+-------------------+
| 3     256   69    |{2679}[67]   8     | 4     1     25    |
| 1     25    7     | 39    25    4     | 6     39    8     |
| 245   24568 689   | 2369  1     259   | 39    7     25    |
+-------------------+-------------------+-------------------+
| 9     678   68    | 678   4     3     | 5     2     1     |
| 25    2568  1     | 2689  68    259-2*| 7     34    34    |
| 257   3     4     | 1    *25*  *257*  | 89    89    6     |
+-------------------+-------------------+-------------------+
| 47    1     5     |[28]   9    *27*   | 38    6     34    |
| 6     47    3     | 5    [78]   1     | 2     48    9     |
| 8     9     2     | 4     3     6     | 1     5     7     |
+-------------------+-------------------+-------------------+

[RW]

There's a very interesting Reverse-BUG in this puzzle:

Code: Select all

 *--------------------------------------------------------------------*
 | 3      256    569    | 2679   2567   8      | 4      1      259    |
 | 1      25     7      | 239    235    4      | 6      359    8      |
 | 2458   24568  5689   | 2369   1      259    | 39     7      2359   |
 |----------------------+----------------------+----------------------|
 | 9      678    68     | 678    4      3      |*5     *2      1      |
 | 258    2568   1      | 2689   2568   259    | 7      34     34     |
 | 257    3      4      | 1      25     257    | 89     89     6      |
 |----------------------+----------------------+----------------------|
 | 47     1      5+8    | 2+38   9      27     |#38     6     -345    |
 | 6      47     3      |*5      78     1      |*2      489    49     |
 | 58     9     *2      | 4      38     6      | 1      5+38   7      |
 *--------------------------------------------------------------------*

The given and solved digits '2' and '5' marked with '*' would all be included in one unavoidable set size 8 if r7c3<>8, r7c4<>38 and r9c8<>38. The ’38’ pair in r7c7 can see all these cells and be used like an UR type 3 to eliminate ’3’ and ’8’ from all other cells that can see all the mentioned cells and the pair => r7c9<>3.

After this there’s a quite simple chain:

If r8c8<>8 => r8c5=8 => r9c5=3 => r7c7=3 => r3c7=9 => r6c8=9 => r8c8<>9

And a question to the nice guys: Is this a correct translation?

[r8c8]=8=[r8c5]-8-[r9c5]-3-[r9c8]=3=[r7c7]-3-[r3c7]-9-[r6c7]=9=[r6c8]-9-[r8c8]

Advances the puzzle here:

Code: Select all

 *--------------------------------------------------------------------*
 | 3      256    569    | 2679   2567   8      | 4      1      25     |
 | 1      25     7      | 239    235    4      | 6      359    8      |
 | 2458   24568  5689   | 2369   1      259    | 39     7      235    |
 |----------------------+----------------------+----------------------|
 | 9      678    68     | 678    4      3      | 5      2      1      |
 | 258    2568   1      | 2689   2568   259    | 7      34     34     |
 | 257    3      4      | 1      25     257    | 89     89     6      |
 |----------------------+----------------------+----------------------|
 | 47     1     *58     | 238    9      27     |-38     6     *45     |
 | 6      47     3      | 5      78     1      | 2     *48     9      |
 | 58     9      2      | 4      38     6      | 1      358    7      |
 *--------------------------------------------------------------------*

And the puzzle is solved by a XY-wing.

[Edit: Just saw tso's solution, his first 4-cell XY-chain together with my Reverse-BUG leaves nothing but singles.]

RW

[RW]

And after tso's first step:

Code: Select all

 *--------------------------------------------------------------------*
 | 3      256    69     | 2679   67     8      | 4      1      25     |
 | 1      25     7      | 39     25     4      | 6      39     8      |
 | 245    24568  689    | 2369   1      259    | 39     7      25     |
 |----------------------+----------------------+----------------------|
 | 9      678    68     | 678    4      3      |*5     *2      1      |
 | 25     2568   1      | 2689   68     259    | 7      34     34     |
 | 257    3      4      | 1      25     257    | 89     89     6      |
 |----------------------+----------------------+----------------------|
 | 47     1     *5      |-28     9      27     | 38     6      34     |
 | 6      47     3      |*5      78     1      |*2      48     9      |
 | 8      9     *2      | 4      3      6      | 1     *5      7      |
 *--------------------------------------------------------------------*

you can also do the basic Reverse-BUG elimination r7c4<>2.

RW

[GregFiore]

Thanks tso, fermat, and RW.
I was able to use forced chains to get it to the state that tso showed just before the series of r1c4<>2 steps.
I usually only force chains to look for cell numbers that "do not change" with each test digit. which is easily recognizable on paper. tso, how did
you know to look at the r1c4 cell, to see that for each r1c5 (6 and 7) the
2 in r1c4 <> 2?? Just trial and error on every affected cell in the puzzle?
RW, what is the Reverse bug?
Thanks again for the help. I will use forced chains to see if any digits can not exist for each trial number.
Greg Fiore

[RW]

RW, what is the Reverse bug?

There's a very interesting Reverse-BUG in this puzzle

The blue word is a link that takes you to a thread that explains the technique.

RW

[tso]

tso, how did
you know to look at the r1c4 cell, to see that for each r1c5 (6 and 7) the
2 in r1c4 <> 2?? Just trial and error on every affected cell in the puzzle?

I didn't know, anymore than I know where to look for a naked triple or even a hidden single. I just search for them more or less systematically. I usually look for the smallest chains first and focus more on bivalue cells because the links are easier to see. If I can't close the chain, I'll see if there's a bilocation link or a more complex link like a pair, etc.

*All* methods are trial and error -- it's just a matter of degree. See http://www.stolaf.edu/people/hansonr/sudoku/index.htm. Finding the second chain was no more or less trial and error than finding the first -- or finding a hidden pair, etc. I could have found the xyz-wing -- but I didn't. There are surely other chains I didn't find. For example:

Code: Select all

 *--------------------------------------------------------------------*
 | 3      256    69     | 2679  [67]    8      | 4      1      25     |
 | 1      25     7      | 39     25     4      | 6      39     8      |
 | 245    24568  689    | 2369   1      259    | 39     7      25     |
 |----------------------+----------------------+----------------------|
 | 9      678    68     |[678]   4      3      | 5      2      1      |
 | 25     2568   1      | 2689  [68]    259    | 7      34     34     |
 | 257    3      4      | 1      25     257    | 89     89     6      |
 |----------------------+----------------------+----------------------|
 | 47     1      5      | 28     9      27     | 38     6      34     |
 | 6      47     3      | 5      78     1      | 2      48     9      |
 | 8      9      2      | 4      3      6      | 1      5      7      |
 *--------------------------------------------------------------------*

The three cells in [brackets] form a short chain.

r4c4=8 -> r5c5=6 -> r1c5=7 -> r1c4<>7 and then I'm stuck -- but wait -- if r1c4<>7, there is only one cell left in that column that can be 7 -- r4c4. But that's a contradiction. So r4c4<>8. This moves the puzzle forward along a different but just as valid solution path.