The New Sudoku Players' Forum

[kb]

Any help with the following would be appreciated

*-----------*
|5.3|9.7|6.4|
|...|...|2.9|
|.9.|.4.|5..|
|---+---+---|
|6..|27.|..5|
|...|.9.|..2|
|...|.31|7.8|
|---+---+---|
|9.5|.6.|42.|
|3.4|..9|856|
|.68|45.|9.1|
*-----------*

[Pat]

- - - - - - -[ 38 clues ]

Code: Select all

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



hi kb,

this puzzle is too tough for me -- expect it needs some Forcing Chains

please use [code] ... [/code] when posting puzzles

[tarek]

a proposed solution......... (assuming the following candidate state):

Code: Select all

*-----------------------------------------------------------------*
| 5      28     3     | 9      128    7     | 6      18     4     |
| 1478   478    167   |#1356   18     356   | 2      1378   9     |
| 1278   9      1267  |*136    4      26-3  | 5      1378  *37    |
|---------------------+---------------------+---------------------|
| 6      348    19    | 2      7      48    | 13     49     5     |
| 1478   34578  17    | 568    9      4568  | 13     46     2     |
| 24     245    29    | 56     3      1     | 7      469    8     |
|---------------------+---------------------+---------------------|
| 9      17     5     |*1378   6      38    | 4      2     *37    |
| 3      127    4     | 17     12     9     | 8      5      6     |
| 27     6      8     | 4      5      23    | 9      37     1     |
*-----------------------------------------------------------------*
Eliminating 3 From r3c6 (Finned XWing in Columns 49 with 1 fin in Box 2)
*-----------------------------------------------------------------*
| 5      28     3     | 9      128    7     | 6      18     4     |
| 1478   478   %167   | 1356   18     356   | 2      1378   9     |
| 1278   9     %1267  | 136    4      6-2   | 5      1378   37    |
|---------------------+---------------------+---------------------|
| 6      348   *19    | 2      7     ^48    | 13    *49     5     |
| 1478   34578 %17    | 568    9      4568  | 13     46     2     |
| 24     245    29    | 56     3      1     | 7      469    8     |
|---------------------+---------------------+---------------------|
| 9      17     5     | 1378   6     ^38    | 4      2      37    |
| 3      127    4     | 17     12     9     | 8      5      6     |
| 27     6      8     | 4      5     ^23    | 9      37     1     |
*-----------------------------------------------------------------*
Eliminating 2 from r3c6(ALS-XY  A=149 in r4c8,r4c3 B=1267 in r5c3,r2c3,r3c3 C=2348 in r4c6,r7c6,r9c6 x=1 y=4 z=2)

Then singles....

tarek

[Carcul]

Any help with the following would be appreciated

Welcome to this forum Kb. Regarding your puzzle:

Code: Select all

 *------------------------------------------------------------*
 | 5      28     3    | 9      128    7    | 6      18     4  |
 | 1478   478    167  | 1356   18     356  | 2      1378   9  |
 | 1278   9      1267 | 136    4      236  | 5      1378   37 |
 |--------------------+--------------------+------------------|
 | 6      348    19   | 2      7      48   | 13     49     5  |
 | 1478   34578  17   | 568    9      4568 | 13     46     2  |
 | 24     245    29   | 56     3      1    | 7      469    8  |
 |--------------------+--------------------+------------------|
 | 9      17     5    | 1378   6      38   | 4      2      37 |
 | 3      127    4    | 17     12     9    | 8      5      6  |
 | 27     6      8    | 4      5      23   | 9      37     1  |
 *------------------------------------------------------------*


We have an Almost Unique Rectangle in cells r7c246/r8c24 (check this post):

[r9c6]-3-[r7c46]=3,8|2=[r8c2]-2-[r9c1]-7-[r9c8]-3-[r9c6],

which implies that r9c6 cannot be "3" and the puzzle is solved.

Carcul

[kb]

Pat wrote:

hi kb,

this puzzle is too tough for me -- expect it needs some Forcing Chains

please use [code] ... [/code] when posting puzzles

[/quote]

Its comforting to see somebody else found this puzzle difficult also.

What does " [code] ... [/code] " mean?

[kb]

a proposed solution......... (assuming the following candidate state):

Code: Select all

*-----------------------------------------------------------------*
| 5      28     3     | 9      128    7     | 6      18     4     |
| 1478   478    167   |#1356   18     356   | 2      1378   9     |
| 1278   9      1267  |*136    4      26-3  | 5      1378  *37    |
|---------------------+---------------------+---------------------|
| 6      348    19    | 2      7      48    | 13     49     5     |
| 1478   34578  17    | 568    9      4568  | 13     46     2     |
| 24     245    29    | 56     3      1     | 7      469    8     |
|---------------------+---------------------+---------------------|
| 9      17     5     |*1378   6      38    | 4      2     *37    |
| 3      127    4     | 17     12     9     | 8      5      6     |
| 27     6      8     | 4      5      23    | 9      37     1     |
*-----------------------------------------------------------------*
Eliminating 3 From r3c6 (Finned XWing in Columns 49 with 1 fin in Box 2)
*-----------------------------------------------------------------*
| 5      28     3     | 9      128    7     | 6      18     4     |
| 1478   478   %167   | 1356   18     356   | 2      1378   9     |
| 1278   9     %1267  | 136    4      6-2   | 5      1378   37    |
|---------------------+---------------------+---------------------|
| 6      348   *19    | 2      7     ^48    | 13    *49     5     |
| 1478   34578 %17    | 568    9      4568  | 13     46     2     |
| 24     245    29    | 56     3      1     | 7      469    8     |
|---------------------+---------------------+---------------------|
| 9      17     5     | 1378   6     ^38    | 4      2      37    |
| 3      127    4     | 17     12     9     | 8      5      6     |
| 27     6      8     | 4      5     ^23    | 9      37     1     |
*-----------------------------------------------------------------*
Eliminating 2 from r3c6(ALS-XY  A=149 in r4c8,r4c3 B=1267 in r5c3,r2c3,r3c3 C=2348 in r4c6,r7c6,r9c6 x=1 y=4 z=2)

Then singles....

tarek

Thanks Tarek - please point me to an explanation of a "finned X wing."

[kb]

Any help with the following would be appreciated

Welcome to this forum Kb. Regarding your puzzle:

Code: Select all

 *------------------------------------------------------------*
 | 5      28     3    | 9      128    7    | 6      18     4  |
 | 1478   478    167  | 1356   18     356  | 2      1378   9  |
 | 1278   9      1267 | 136    4      236  | 5      1378   37 |
 |--------------------+--------------------+------------------|
 | 6      348    19   | 2      7      48   | 13     49     5  |
 | 1478   34578  17   | 568    9      4568 | 13     46     2  |
 | 24     245    29   | 56     3      1    | 7      469    8  |
 |--------------------+--------------------+------------------|
 | 9      17     5    | 1378   6      38   | 4      2      37 |
 | 3      127    4    | 17     12     9    | 8      5      6  |
 | 27     6      8    | 4      5      23   | 9      37     1  |
 *------------------------------------------------------------*


We have an Almost Unique Rectangle in cells r7c246/r8c24 (check this post):

[r9c6]-3-[r7c46]=3,8|2=[r8c2]-2-[r9c1]-7-[r9c8]-3-[r9c6],

which implies that r9c6 cannot be "3" and the puzzle is solved.

Carcul

Thanks Carcul. I briefly checked the AUR post - looks like I've got my work cut out for me.

[tarek]

Thanks Tarek - please point me to an explanation of a "finned X wing."

you will understand finned x-wing if you master basic x-wings first........

You probably do but there was no indication that you do or that you used any from the grid you submitted.......

A thread here has an amazing description of the basic x-wing with a nice example.... your puzzle also has one & other finned x-wings.

for the finned x-wing ....try here.
& the ultimate fish thread should answer everything when it is complete


tarek

[kb]

Thanks Tarek - please point me to an explanation of a "finned X wing."

you will understand finned x-wing if you master basic x-wings first........

You probably do but there was no indication that you do or that you used any from the grid you submitted.......

A thread here has an amazing description of the basic x-wing with a nice example.... your puzzle also has one & other finned x-wings.

for the finned x-wing ....try here.
& the ultimate fish thread should answer everything when it is complete


tarek

I see it! A thing of beauty indeed, thank you.

[JeffInCA]

kb / tarek / Carul,

This was an interesting puzzle.

I was able to eliminate 3 from r3c6 as tarek indicated (however, I used coloring for my elimination)

The 2nd elimination was a bit trickier. Tarek, the ALS-XY mechanism seems quite complicated to do just looking at a puzzle. Do you spot this by looking or with the use of a programmatic solver?

The AUR mechanism as described by Carcul seems a bit more intuitive and easier to spot with the naked eye, as I like to solve puzzles - just using that with candidate elimination.

I didn't spot it at first but once applying AUR I was also able to eliminate the 2 from r3c6 (and I can see how you can also eliminate 3 from r6c9 using the same process)

One final question. I'm still a bit confused by some of the notation that many on this board use to describe chains.

For example from Carcul's post:

[r9c6]-3-[r7c46]=3,8|2=[r8c2]-2-[r9c1]-7-[r9c8]-3-[r9c6]

Is there some place where this notation is explained? What I'm most concerned with is the use of - vs. = and how to read this in terms of "implies" or "implies NOT", etc.

I'd say I get it about 80-90% but it would help if I could read an explanation somewhere.

Thanks,

Jeff

[tarek]

Tarek, the ALS-XY mechanism seems quite complicated to do just looking at a puzzle. Do you spot this by looking or with the use of a programmatic solver?

In this specific occasion it was the latter (my solver, which I programmed) & to be honest, I struggle greatly to spot ALS-xy. the only way I do spot them, is when I'm looking for almost locked cells around an elimination cell of interest. so they can be as difficult as finding some forcing chains if not more difficult

Still, difficult. I wouldn't spot it if there are other simpler techniques present.

tarek

[JeffInCA]

tarek,

Thanks for the sanity check

Jeff

[ronk]

The AUR mechanism as described by Carcul seems a bit more intuitive and easier to spot with the naked eye, as I like to solve puzzles - just using that with candidate elimination.

I didn't spot it at first but once applying AUR I was also able to eliminate the 2 from r3c6 (and I can see how you can also eliminate 3 from r6c9 using the same process)

Then you might appreciate using the four strong links for the UR digits to obtain four eliminatons.

Code: Select all

 .   ab    .   | .    ab+X .
    a|         |           
 .   |.    .   | .    .    .
     |         |           
 .   ab+Y  .   | .    ab   .

If the puzzle is to have a unique solution, at least one of the (possibly multiple) 'X' and 'Y' candidates must be true. If an 'X' digit is true, 'a' is excluded from the ab+X cell. If a 'Y' digit is true, 'a' is still excluded from the ab+X cell due to the strong link in 'a'.

Code: Select all

 5     28     3   | 9     128  7   | 6   18    4
 1478  478    167 | 1356  18   356 | 2   1378  9
 1278  9      1267| 136   4    236 | 5   1378  37
------------------+----------------+--------------
 6     348    19  | 2     7    48  | 13  49    5
 1478  34578  17  | 568   9    4568| 13  46    2
 24    245    29  | 56    3    1   | 7   469   8
------------------+----------------+--------------
 9    *17     5   |*1378  6    38  | 4   2     37
 3    *127    4   |*17    12   9   | 8   5     6
 27    6      8   | 4     5    23  | 9   37    1

Because of the strong links in '1' in r7 and c2, r8c2<>1 and r7c4<>1 ... and because of the strong links in '7' in r8 and c4, r7c4<>7 and r8c2<>7.

[daj95376]

Another solution. Unfortunately, nothing special about it.

Code: Select all

# After SSTS: Naked Pair, Locked Candidates (1)
# optional  : Locked Candidates (2), X-Wing, and Colors on <3> and <7>
#
# 3-[r7c6]-8-[r4c6]-4-[r4c8]-9-[r4c3]-1-[r4c7]-3-[r4c2]-8-[r1c2]-2-[r3c3] => [c3] Invalid!
# Therefore, [r7c6]=3 and the puzzle solves with a cascade of Singles
 *--------------------------------------------------------------------*
 | 5     g28     3      | 9      128    7      | 6      18     4      |
 | 1478   478    167    | 1356   18     356    | 2      1378   9      |
 | 128    9      1267   | 136    4      26     | 5      1378   37     |
 |----------------------+----------------------+----------------------|
 | 6     f348   d19     | 2      7     b48     |e13    c49     5      |
 | 1478   34578  17     | 568    9      4568   | 13     46     2      |
 | 24     45     29     | 56     3      1      | 7      469    8      |
 |----------------------+----------------------+----------------------|
 | 9      17     5      | 1378   6     a38     | 4      2      37     |
 | 3      127    4      | 17     12     9      | 8      5      6      |
 | 27     6      8      | 4      5      23     | 9      37     1      |
 *--------------------------------------------------------------------*


[udosuk]

Code: Select all

 *--------------------------------------------------------------------*
 | 5      28     3      | 9      128    7      | 6      18     4      |
 | 1478   478    167    | 1356   18     356    | 2      1378   9      |
 | 1278   9      1267   | 136    4      236    | 5      1378   37     |
 |----------------------+----------------------+----------------------|
 | 6      348    19     | 2      7      48     | 13     49     5      |
 | 1478   34578  17     | 568    9      4568   | 13     46     2      |
 | 24     245    29     | 56     3      1      | 7      469    8      |
 |----------------------+----------------------+----------------------|
 | 9     #17     5      |#1378   6     *38     | 4      2      37     |
 | 3     #127    4      |#17    -12     9      | 8      5      6      |
 | 27     6      8      | 4      5     *23     | 9      37     1      |
 *--------------------------------------------------------------------*

Along Carcul's line of almost UR, but with simpler logic:

r8c5=2 => r9c6=3 => r7c6=8 => {17} in r78c24
Therefore r8c5<>2, must be 1...