The New Sudoku Players' Forum

[Jasper32]

I have tried everything in my "tool box" and cannot solve this puzzle. This seems like a tough puzzle to me. I would appreciate any comments or help you can give me. Thank you.

*-----------*
|1..|...|..6|
|.6.|4..|.3.|
|..7|.2.|8..|
|---+---+---|
|..9|583|4..|
|...|2.6|...|
|..4|917|6..|
|---+---+---|
|..1|.3.|2..|
|.8.|..4|.9.|
|5..|...|..1|
*-----------*


*-----------*
|14.|3.8|9.6|
|.68|4..|.3.|
|..7|62.|8.4|
|---+---+---|
|6.9|583|4..|
|7..|246|.89|
|8.4|917|6.3|
|---+---+---|
|491|735|268|
|.8.|164|.9.|
|576|892|341|
*-----------*


*--------------------------------------------------*
| 1 4 25 | 3 57 8 | 9 27 6 |
| 29 6 8 | 4 57 19 | 157 3 257 |
| 39 35 7 | 6 2 19 | 8 15 4 |
|----------------+----------------+----------------|
| 6 12 9 | 5 8 3 | 4 127 27 |
| 7 13 35 | 2 4 6 | 15 8 9 |
| 8 25 4 | 9 1 7 | 6 25 3 |
|----------------+----------------+----------------|
| 4 9 1 | 7 3 5 | 2 6 8 |
| 23 8 23 | 1 6 4 | 57 9 57 |
| 5 7 6 | 8 9 2 | 3 4 1 |
*--------------------------------------------------*

[Cec]

Hi Jasper,
Firstly, if you "wrap" your puzzle between the code buttons your pencilmark grid will look like this

Code: Select all

 *--------------------------------------------------*
 | 1    4    25   | 3    57   8    | 9    27   6    |
 | 29   6    8    | 4    57   19   | 157  3    257  |
 | 39   35   7    | 6    2    19   | 8    15   4    |
 |----------------+----------------+----------------|
 | 6    12   9    | 5    8    3    | 4    127  27   |
 | 7    13   35   | 2    4    6    | 15   8    9    |
 | 8    25   4    | 9    1    7    | 6    25   3    |
 |----------------+----------------+----------------|
 | 4    9    1    | 7    3    5    | 2    6    8    |
 | 23   8    23   | 1    6    4    | 57   9    57   |
 | 5    7    6    | 8    9    2    | 3    4    1    |
 *--------------------------------------------------*

As to solving this puzzle, advanced techniques have been beyond me but have recently been reading a bit more on some of these techniques such as the "finned x-wing" pattern. I'm wondering whether such a pattern exists for the candidate 5's which I've highlighted * as follows in columns 7 and 9:

Code: Select all

 *--------------------------------------------------*
 | 1    4    25   | 3    57   8    | 9    27   6    |
 | 29   6    8    | 4  **57   19   | 15*7  3   25*7 |
 | 39   35   7    | 6    2    19   | 8    15   4    |
 |----------------+----------------+----------------|
 | 6    12   9    | 5    8    3    | 4    127  27   |
 | 7    13   35   | 2    4    6      15(X)8    9    |
 | 8    25   4    | 9    1    7    | 6    25   3    |
 |----------------+----------------+----------------|
 | 4    9    1    | 7    3    5    | 2    6    8    |
 | 23   8    23   | 1    6    4    | 5*7   9   5*7  |
 | 5    7    6    | 8    9    2    | 3    4    1    |
 *--------------------------------------------------*

My question is whether candidate 5 in cell r2c5 forms a finned x-wing for the 5's [rows 2 and 8 and columns 7 and 9) which then allows candidate 5 to be excluded from r5c7 and thus solve the puzzle after the placement of digit 1 in cell r5c7 ?

Cec

[Pat]

have recently been reading a bit more on some of these techniques such as the "finned x-wing" pattern.
I'm wondering whether such a pattern exists for the candidate 5s in columns 7 and 9:

Code: Select all

 *--------------------------------------------------*
 | 1    4    25   | 3    57   8    | 9    27   6    |
 | 29   6    8    | 4   #57   19   | 1*57 3    2*57 |
 | 39   35   7    | 6    2    19   | 8    15   4    |
 |----------------+----------------+----------------|
 | 6    12   9    | 5    8    3    | 4    127  27   |
 | 7    13   35   | 2    4    6      1-5  8    9    |
 | 8    25   4    | 9    1    7    | 6    25   3    |
 |----------------+----------------+----------------|
 | 4    9    1    | 7    3    5    | 2    6    8    |
 | 23   8    23   | 1    6    4    | *57  9    *57  |
 | 5    7    6    | 8    9    2    | 3    4    1    |
 *--------------------------------------------------*



My question is whether candidate 5 in cell r2c5 forms a finned x-wing for the 5s (rows 2 and 8 and columns 7 and 9) which then allows candidate 5 to be excluded from r5c7 ?

well it could be considered a finned X-wing,
but it does not exclude the 5 at r5c7

[Cec]

".....well it could be considered a finned X-wing,
but it does not exclude the 5 at r5c7

Thanks Pat for your reply. Is it candidate 5 in r2c5 that can be excluded?

Cec

[Pat]

".....well it could be considered a finned X-wing,
but it does not exclude the 5 at r5c7

Is it candidate 5 in r2c5 that can be excluded?

sorry i should have been more explicit --

it could be considered a finned X-wing,
but it does not exclude anything.

if you're looking for a fancy exclusion of a 5,
try an "XYZ-wing" --

r2c7 is either itself 5 or (check its other possible values) forces a 5 in r2c5 or in r3c8;
therefore, 5 is excluded at r2c9 (cell which sees all of the above 3 cells).

[Steve R]

Perhaps the simplest way to solve the puzzle is to use a W-Wing.

The key to the wing is to look for two cells with the same two candidates which do not share a house; then to see whether there is a link between them.

The puzzle contains several examples of such cells. Some are not much help because they lack a useful link but consider the (25) in r1c3 and r6c8:

Code: Select all

 *--------------------------------------------------*
 | 1    4    25*  | 3    57   8    | 9    27   6    |
 | 29   6    8    | 4    57   19   | 157  3    257  |
 | 39   35   7    | 6    2    19   | 8    15   4    |
 |----------------+----------------+----------------|
 | 6    12   9    | 5    8    3    | 4    127  27   |
 | 7    13   35   | 2    4    6    | 15   8    9    |
 | 8    25   4    | 9    1    7    | 6    25*  3    |
 |----------------+----------------+----------------|
 | 4    9    1    | 7    3    5    | 2    6    8    |
 | 23   8    23   | 1    6    4    | 57   9    57   |
 | 5    7    6    | 8    9    2    | 3    4    1    |
 *--------------------------------------------------*

The link between them is provided by column 2. Only two cells in that column are open to 5. If r3c2 contains 5, then r1c3 contains 2; on the other hand, if r6c2 contains 5, r6c8 contains 2.

Whichever applies, 2 may be eliminated from r1c8 and this is sufficient to solve the puzzle.

Steve

[Jasper32]

Thanks to all. I was wondering if the following could be a vaid chain:

r8c7=5, r8c9=7, r4c9=2. r6c8=5 then 5 could be eliominated from r5c7

This works to eliminate that 5 but was this a valid chain or just a lucky guess. I had a 50-50 chance on this so I am not sure???

[Cec]

To Pat and Steve.. thanks for the lifebuoy. I knew I was getting in over my head but at least the puzzle has been solved with more homework for me.

Cec

[Steve R]

Jasper,

The chain is OK but, as I read it, it means that, if r8c7 = 5, r6c8 = 5 and I am not clear how the elimination follows.

A possible XY-chain alternative is:

r6c8 = 2 ==> r6c2 = 5 ==> r5c3 = 3 ==> r8c3 = 2 ==> r1c3 = 5 ==> r1c5 = 7 ==> r1c8 = 2 ==> r6c8 ≠ 2.

The contradiction means that 2 may be eliminated from r6c8

Steve

[daj95376]

While everyone else is concentrating on solving the original PM, I'm curious how Jasper32 managed to get the original puzzle past this point ... and then end up snared by an XYZ-Wing.

Code: Select all

 *-----------*
 |1..|...|..6|
 |.6.|4..|.3.|
 |..7|.2.|8..|
 |---+---+---|
 |..9|583|4..|
 |...|2.6|...|
 |..4|917|6..|
 |---+---+---|
 |..1|.3.|2..|
 |.8.|..4|.9.|
 |5..|...|..1|
 *-----------*

 *--------------------------------------------------------------------*
 | 1      2459   258    | 3      57     89     | 579    2457   6      |
 | 289    6      258    | 4      57     189    | 1579   3      2579   |
 | 349    359    7      | 6      2      19     | 8      15     459    |
 |----------------------+----------------------+----------------------|
 | 6      127    9      | 5      8      3      | 4      127    27     |
 | 378    1357   358    | 2      4      6      | 1579   1578   35789  |
 | 238    235    4      | 9      1      7      | 6      258    2358   |
 |----------------------+----------------------+----------------------|
 | 479    79     1      | 78     3      5      | 2      6      48     |
 | 237    8      23     | 1      6      4      | 357    9      57     |
 | 5      347    6      | 78     9      2      | 37     48     1      |
 *--------------------------------------------------------------------*


[Jasper32]

I went back on this puzzle and found the next removal, from the puzzle you sent, was the (4) in
in r7c9. For the life of me I cannot figure out how I arrived at that nor what prompted me to do so. I thought that perhaps there was am ALS in box 3 and box 9 but that doesn't seem to work. I must have spent a total of 7 hours on this puzzle and I do know I used AIC's someplace and a couple of ALS's to get to where I gave up. I worked so long on this it has becomes a muddle. Also, I don't understand about the the XYZ-Wing you mentioned. I don't think that was something I found. Could you please explain where the XYZ-Wing was located. To say that this puzzle has left me bewildered is a masterpiece of understatement. Also, as yet I have not gotten a reply as to whether the forcing chain was valid or not. I do think I used at least one of these as well ........someplace in working on the puzzle.

[daj95376]

I don't understand about the the XYZ-Wing you mentioned. I don't think that was something I found. Could you please explain where the XYZ-Wing was located.

if you're looking for a fancy exclusion of a 5,
try an "XYZ-wing" --

r2c7 is either itself 5 or (check its other possible values) forces a 5 in r2c5 or in r3c8;
therefore, 5 is excluded at r2c9 (cell which sees all of the above 3 cells).

Code: Select all

+-----------------------------------------------------------+
|  1     4     25   |  3     57    8    |  9     27    6    |
|  29    6     8    |  4    *57    19   | *157   3     27-5 |
|  39    35    7    |  6     2     19   |  8    *15    4    |
|-------------------+-------------------+-------------------|
|  6     12    9    |  5     8     3    |  4     127   27   |
|  7     13    35   |  2     4     6    |  15    8     9    |
|  8     25    4    |  9     1     7    |  6     25    3    |
|-------------------+-------------------+-------------------|
|  4     9     1    |  7     3     5    |  2     6     8    |
|  23    8     23   |  1     6     4    |  57    9     57   |
|  5     7     6    |  8     9     2    |  3     4     1    |
+-----------------------------------------------------------+
r2c9    <> 5     XYZ-Wing   on [r2c7]
r8c9    =  5     Hidden Single
r8c7    =  7     Naked  Single
r4c8    =  2     BUG+1
                 Naked Singles


[Jasper32]

Wow....Thanks alot. I completely missed the XYZ Wing. I appreciate everybody's help and suggestions. It is kind of you to take your time to help me. Thanks again.

[daj95376]

How about a Unique Rectangle elimination for [r2c9]<>5 ?

Code: Select all

 *--------------------------------------------------*
 | 1    4    25   | 3    57   8    | 9    27   6    |
 | 29   6    8    | 4    57   19   |*57+1 3   *57+2 |
 | 39   35   7    | 6    2    19   | 8    15   4    |
 |----------------+----------------+----------------|
 | 6    12   9    | 5    8    3    | 4    127  27   |
 | 7    13   35   | 2    4    6    | 15   8    9    |
 | 8    25   4    | 9    1    7    | 6    25   3    |
 |----------------+----------------+----------------|
 | 4    9    1    | 7    3    5    | 2    6    8    |
 | 23   8    23   | 1    6    4    |*57   9   *57   |
 | 5    7    6    | 8    9    2    | 3    4    1    |
 *--------------------------------------------------*


Unique Rectangle in [r28c79] based on digits 57. Therefore, ...

Code: Select all

[r2c7]=1 => [r3c8]=5 => [r2c9]<>5   -or-
[r2c9]=2 =>             [r2c9]<>5


[Jasper32]

Yes, I missed that as well. I am learning a lot from this forum. Still nobody has replied to a previous post where I asked if the forcing chain of:

r8c7=5 >r8c9=7>r4c9=2>r6c8=5>r5c7<>5

is valid. I am curious if I did that correctly.

*--------------------------------------------------*
| 1 4 25 | 3 57 8 | 9 27 6 |
| 29 6 8 | 4 57 19 |*57+1 3 *57+2 |
| 39 35 7 | 6 2 19 | 8 15 4 |
|----------------+----------------+----------------|
| 6 12 9 | 5 8 3 | 4 127 27 |
| 7 13 35 | 2 4 6 | 15 8 9 |
| 8 25 4 | 9 1 7 | 6 25 3 |
|----------------+----------------+----------------|
| 4 9 1 | 7 3 5 | 2 6 8 |
| 23 8 23 | 1 6 4 |*57 9 *57 |
| 5 7 6 | 8 9 2 | 3 4 1 |
*--------------------------------------------------*

[/code]