The New Sudoku Players' Forum

[Fortesque92]

Hello everyone,

First time posting. Stuck on this puzzle and looking for some assistance. I've used Snyder notation to mark up empty cells and have scanned every row, column and box for numbers but still stumped. Have I missed something?

Cheers,
Geordan

[qiuyanzhe]

Skyscrapers(Remote Pair) on 4 and 6,
r6c9==r2c9--r2c5==r5c5
deletes r5c8(46)

so r5c8=3

[Leren]

Code: Select all

*-----------*
|..5|2..|8..|
|891|..3|2..|
|...|...|..9|
|---+---+---|
|1.2|...|...|
|.79|8..|1.2|
|...|..9|...|
|---+---+---|
|...|.5.|4.7|
|..7|.3.|915|
|2..|.1.|..3|
*-----------*

I think this is what your PM diagram should show :

Code: Select all

*----------------------------------------*
| 347 34  5 | 2   9   a46  | 8  b3467 1  |
| 8   9   1 | 57  4-6  3   | 2   57   46 |
| 347 2   6 | 57  8    1   | 37  3457 9  |
|-----------+--------------+-------------|
| 1   46  2 | 3   7    4-6 | 5   9    8  |
| 34  7   9 | 8  d46   5   | 1  c346  2  |
| 5   346 8 | 1   2    9   | 37  3467 46 |
|-----------+--------------+-------------|
| 9   1   3 | 6   5    8   | 4   2    7  |
| 6   8   7 | 4   3    2   | 9   1    5  |
| 2   5   4 | 9   1    7   | 6   8    3  |
*----------------------------------------*

As was mentioned above, there is a Skyscraper on 6 in cells a-b-c-d; one of a or d must be 6, so r2c5 & r4c6 <> 6. The puzzle solves easily after that.

Leren

[SpAce]

I think this is what your PM diagram should show...

full pencil marks: Show

Code: Select all

.-------------.------------.--------------.
| 347  34   5 | 2   9   46 | 8   3467  1  |
| 8    9    1 | 57  46  3  | 2   57    46 |
| 347  2    6 | 57  8   1  | 37  3457  9  |
:-------------+------------+--------------:
| 1    46   2 | 3   7   46 | 5   9     8  |
| 34   7    9 | 8   46  5  | 1   346   2  |
| 5    346  8 | 1   2   9  | 37  3467  46 |
:-------------+------------+--------------:
| 9    1    3 | 6   5   8  | 4   2     7  |
| 6    8    7 | 4   3   2  | 9   1     5  |
| 2    5    4 | 9   1   7  | 6   8     3  |
'-------------'------------'--------------'


Actually not. The original poster just said he's using the Snyder notation so we should stick to that. It's quite enough to solve this anyway, even in the incomplete form he presented. In fact, it's the best in this case, because it shows only what's needed and not much more. (Well, in this case a decent manual player doesn't need pencil marks at all.)

If I've understood it correctly, this would be the completed Snyder notation (dots denote cells with unmarked candidates):

completed Snyder notation: Show

Code: Select all

.-------------.------------.-------------.
| .7   .3   5 | 2   9   46 | 8   .67  1  |
|  8    9   1 | 57  46  3  | 2    57  46 |
| .47   2   6 | 57  8   1  | 37  .45  9  |
:-------------+------------+-------------:
|  1    46  2 | 3   7   46 | 5    9   8  |
| .3    7   9 | 8   46  5  | 1   .36  2  |
|  5   .6   8 | 1   2   9  | 37  .7   46 |
:-------------+------------+-------------:
|  9    1   3 | 6   5   8  | 4    2   7  |
|  6    8   7 | 4   3   2  | 9    1   5  |
|  2    5   4 | 9   1   7  | 6    8   3  |
'-------------'------------'-------------'

Yet even that's not necessary because a solution is actually easiest to see with the original, incomplete pencil marks:

Code: Select all

.------------.-------------.-------------.
| .7  ..   5 | 2   9    46 | 8   ..  1   |
|  8   9   1 | 57  46*  3  | 2   ..  46* |
| .7   2   6 | 57  8    1  | 37  ..  9   |
:------------+-------------+-------------:
|  1   46  2 | 3   7    46 | 5    9  8   |
| ..   7   9 | 8   46*  5  | 1   ..  2   |
|  5  .6   8 | 1   2    9  | 37  .7  46* |
:------------+-------------+-------------:
|  9   1   3 | 6   5    8  | 4    2  7   |
|  6   8   7 | 4   3    2  | 9    1  5   |
|  2   5   4 | 9   1    7  | 6    8  3   |
'------------'-------------'-------------'

The obvious solution for a manual player (with or without pm) is what qiuyanzhe suggested:

Remote Pair (i.e. Dual Skyscraper) (46)c59 -> -46 r5c8 => +3 r5c8; stte

The power of the Snyder notation is in that it keeps easy things easy by not cluttering the grid with unnecessary details. Of course it's not enough for more serious solving, but then it can be completed.

(Btw, I don't actually use the Snyder notation even in p&p solving because I have my own system, but I can easily see its benefits. It's actually very close to what I used a long time ago, without ever having heard of it, before I developed my current p&p system. I could still use it as part of it too, but I almost never do. I would, though, if speed-solving was my goal.)

As was mentioned above, there is a Skyscraper on 6 in cells a-b-c-d; one of a or d must be 6, so r2c5 & r4c6 <> 6. The puzzle solves easily after that.

It's a different Skyscraper from what qiuyanzhe (and I) suggested, and one that's not visible in the original pencil marks at all. It is available in the completed Snyder notation as well as the full pm (of course), but either way the Remote Pair is the easiest to spot. By far.

Btw, it's interesting that this is a second post in a row that mentions the Snyder notation. What's going on?

[tarek]

Here are the 2 skyscrapers mentioned that would combine into a remote pair:

[Fortesque92]

Ok thanks, everyone! I appreciate everyone taking the time to respond!

[Fortesque92]

Stuck again. I think I've spotted an X Wing with the 3's and an X Wing with the 8's? But not sure what to do with them!

[SpAce]

Stuck again. I think I've spotted an X Wing with the 3's and an X Wing with the 8's? But not sure what to do with them!

This puzzle gets solved with basic techniques only, so no X-Wings or anything needed. The completed Snyder notation might help you see what you're missing:

Code: Select all

1...3.4....97........1.6..36..98...1..3.....95..61...........62982...3.473..2..8.

.-----------.------------.---------------.
| 1  67  5  | 8  3    29 | 4     29.  67 |
| 3  46  9  | 7  45   2. | 128.  1.   68 |
| 2  47  8  | 1  49.  6  | .     9.   3  |
:-----------+------------+---------------:
| 6  2   47 | 9  8    3. | .     3.   1  |
| 8  1   3  | 2  7.   .  | 6     .    9  |
| 5  9   47 | 6  1    3. | 28.   23.  78 |
:-----------+------------+---------------:
| 4  5   1  | 3  79   8  | 79    6    2  |
| 9  8   2  | 5  6    17 | 3     17   4  |
| 7  3   6  | 4  2    19 | 19    8    5  |
'-----------'------------'---------------'
                           28


full pencil marks: Show

Code: Select all

.-----------.--------------.----------------.
| 1  67  5  | 8  3    29   | 4     279   67 |
| 3  46  9  | 7  45   245  | 1258  125   68 |
| 2  47  8  | 1  459  6    | 579   579   3  |
:-----------+--------------+----------------:
| 6  2   47 | 9  8    3457 | 57    3457  1  |
| 8  1   3  | 2  457  457  | 6     457   9  |
| 5  9   47 | 6  1    347  | 278   2347  78 |
:-----------+--------------+----------------:
| 4  5   1  | 3  79   8    | 79    6     2  |
| 9  8   2  | 5  6    17   | 3     17    4  |
| 7  3   6  | 4  2    19   | 19    8     5  |
'-----------'--------------'----------------'

Note that there are only two of both 2 and 8 in column 7 and they're in the same cells. That's a hidden pair (28)r26c7 allowing you to eliminate other candidates from those two cells. After that it's just singles. The key elimination is the 1 in r2c7.

This example also shows the limits of (this version of) the Snyder notation and why I don't use it. It tells you that the 2 and 8 in r2c7 and r6c7 are bilocated somehow (because they're marked), but it doesn't tell you in which ways. Thus it's not obvious that they're both bilocated in the column (which makes them a hidden pair). In my own mark-up system that would be obvious immediately, and the original version of the Snyder notation might show it too (but it has other problems). As far as I know, both are only available in pencil and paper solving, though.

PS. You're right that there's technically an X-Wing in both 3s and 8s but they have nothing to eliminate. Furthermore, since they're both located within single chutes, their potential eliminations would be available with basic intersection techniques. Single-chute X-Wings are good spotting aids for claiming situations, though.

[Fortesque92]

Thank you my friend!