The New Sudoku Players' Forum

[SteveG48]

Here's one that I stumbled onto. It was generated by HoDoKu and I saw that it has a "single advanced move" solution at my level. You folks will probably solve it in your sleep.

Code: Select all

 *-----------*
 |53.|...|.87|
 |...|.93|5..|
 |...|...|9.6|
 |---+---+---|
 |92.|78.|...|
 |...|...|...|
 |...|.69|.71|
 |---+---+---|
 |1.6|...|...|
 |..8|37.|...|
 |35.|...|.64|
 *-----------*


[ArkieTech]

Code: Select all

 *-----------------------------------------------------------*
 | 5     3     9     | 6     124   12    | 14    8     7     |
 |*67   *1678  147   | 148   9     3     | 5     14    2     |
 | 28    18    124   | 1458  145   7     | 9     3     6     |
 |-------------------+-------------------+-------------------|
 | 9     2     135   | 7     8     145   | 6     45    35    |
 |*67   *167   157   | 1245  3     1245  | 248   2459  589   |
 | 48    4-8   35    | 25    6     9     | 23    7     1     |
 |-------------------+-------------------+-------------------|
 | 1     79    6     | 245   245   2458  | 378   29    38    |
 | 24    49    8     | 3     7     6     | 12    1259  59    |
 | 3     5     27    | 9     12    128   | 78    6     4     |
 *-----------------------------------------------------------*
67dp:r25c12 => -8r6c2; ste

[Marty R.]

Code: Select all

+---------------+---------------+--------------+
| 5   3     9   | 6    124 124  | 14  8    7   |
| 67  14678 147 | 148  9   3    | 5   14   2   |
| 248 148   124 | 1458 145 7    | 9   3    6   |
+---------------+---------------+--------------+
| 9   2     135 | 7    8   145  | 6   45   35  |
| 67  167   157 | 1245 3   1245 | 248 2459 589 |
| 48  48    35  | 25   6   9    | 23  7    1   |
+---------------+---------------+--------------+
| 1   79    6   | 2458 245 2458 | 378 29   38  |
| 24  49    8   | 3    7   6    | 12  1259 59  |
| 3   5     27  | 9    12  128  | 78  6    4   |
+---------------+---------------+--------------+


Play this puzzle online at the Daily Sudoku site

In addition to the 67 DP, which I would've called a Type 4 UR=>r25c2<>7:

DP (12)r19c56 8r9c6=4r1c56-(4=1)r1c7-(1=2)r8c7-r8c1=2r9c3-(21=8)r9c56=>r9c6=8

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 5     3     9      | 6     124   124    | 14    8     7      |
|*67   *67+18  147   | 148   9     3      | 5     14    2      |
| 28   #18    124    | 1458  145   7      | 9     3     6      |
|--------------------+--------------------+--------------------|
| 9     2     135    | 7     8     145    | 6     45    35     |
|*67   *67+1  157    | 1245  3     1245   | 248   2459  589    |
| 48    4-8   35     | 25    6     9      | 23    7     1      |
|--------------------+--------------------+--------------------|
| 1     79    6      | 245   245   2458   | 378   29    38     |
| 24    49    8      | 3     7     6      | 12    1259  59     |
| 3     5     27     | 9     12    128    | 78    6     4      |
*--------------------------------------------------------------*

I see this as a UR Type 3. The killers are (18) in r25c2 which forms a (18) pseudo-cell and together with the bi-value cell (18) in r3c2 excludes 18 from the rest of Column 2. Hodoku agrees.

Leren

[Marty R.]

Code: Select all

*--------------------------------------------------------------*
| 5     3     9      | 6     124   124    | 14    8     7      |
|*67   *67+18  147   | 148   9     3      | 5     14    2      |
| 28   #18    124    | 1458  145   7      | 9     3     6      |
|--------------------+--------------------+--------------------|
| 9     2     135    | 7     8     145    | 6     45    35     |
|*67   *67+1  157    | 1245  3     1245   | 248   2459  589    |
| 48    4-8   35     | 25    6     9      | 23    7     1      |
|--------------------+--------------------+--------------------|
| 1     79    6      | 245   245   2458   | 378   29    38     |
| 24    49    8      | 3     7     6      | 12    1259  59     |
| 3     5     27     | 9     12    128    | 78    6     4      |
*--------------------------------------------------------------*

I see this as a UR Type 3. The killers are (18) in r25c2 which forms a (18) pseudo-cell and together with the bi-value cell (18) in r3c2 excludes 18 from the rest of Column 2. Hodoku agrees.

Leren

Leren,

We're both right. It fits the classic definition of a Type 4 because 6 is a strong link in c2. However, a Type 4 can always be played as a Type 3 at the player's discretion. I learned my basic rectangle stuff from Keith's article.

[SteveG48]

The way I thought of it myself was UR(4) r25c12/ALS(r2c2,r5c2,r3c2) => r6c2 <> 8

[Leren]

The way I thought of it myself was UR(4) r25c12/ALS(r2c2,r5c2,r3c2) => r6c2 <> 8

The way you have played this is as a UR Type 3 (according to the Hodoku classification system of URs). As I said above I put this into Hodoku and they played it this way.
I also played the Type 3 because, well, 3 comes before 4, so that's my solving order, even though it might be argued that a Type 4 is a simpler pattern than a Type 3.

BTW here is a non-uniqueness based single move solution, which I would normally play before looking for uniqueness moves:

Code: Select all

*--------------------------------------------------------------*
| 5     3     9      | 6     124   124    |a14    8     7      |
| 67    1678  147    | 148   9     3      | 5    b14    2      |
| 28    18    124    | 1458  145   7      | 9     3     6      |
|--------------------+--------------------+--------------------|
| 9     2     135    | 7     8     145    | 6     45    35     |
| 67    167   157    | 1245  3     1245   |f28-4  2459 e589    |
| 48    48    35     | 25    6     9      | 23    7     1      |
|--------------------+--------------------+--------------------|
| 1     79    6      | 245   245   2458   | 378   29    38     |
| 24    49    8      | 3     7     6      | 12   c1259 d59     |
| 3     5     27     | 9     12    128    | 78    6     4      |
*--------------------------------------------------------------*

(4) r1c7 = (4-1) r2c8 = (1-5) r8c8 = (5-9) r8c9 = (9-8) r5c9 = (8) r5c7 => - 4 r5c7; lclste

Leren

[SteveG48]

BTW here is a non-uniqueness based single move solution, which I would normally play before looking for uniqueness moves:

Code: Select all

*--------------------------------------------------------------*
| 5     3     9      | 6     124   124    |a14    8     7      |
| 67    1678  147    | 148   9     3      | 5    b14    2      |
| 28    18    124    | 1458  145   7      | 9     3     6      |
|--------------------+--------------------+--------------------|
| 9     2     135    | 7     8     145    | 6     45    35     |
| 67    167   157    | 1245  3     1245   |f28-4  2459 e589    |
| 48    48    35     | 25    6     9      | 23    7     1      |
|--------------------+--------------------+--------------------|
| 1     79    6      | 245   245   2458   | 378   29    38     |
| 24    49    8      | 3     7     6      | 12   c1259 d59     |
| 3     5     27     | 9     12    128    | 78    6     4      |
*--------------------------------------------------------------*

(4) r1c7 = (4-1) r2c8 = (1-5) r8c8 = (5-9) r8c9 = (9-8) r5c9 = (8) r5c7 => - 4 r5c7; lclste

Leren

You would spot that before glomming on to a simple DP possible? Holy cow!

[Leren]

SteveG48 wrote: You would spot that before glomming on to a simple DP possible?

I always look for moves that don't rely on uniqueness before those that do. Have look here http://sudopedia.enjoysudoku.com/Uniqueness_Controversy.html

Leren

[daj95376]

_

I've read numerous pro/con arguments over the years over Uniqueness Testing. Here's my position on the topic.

If I post a solution with eliminations based on Uniqueness Testing, and you can find a solution using the DP pattern that I treated as invalid, then please post your solution!

Regards, Danny A. Jones

[SteveG48]

SteveG48 wrote: You would spot that before glomming on to a simple DP possible?

I always look for moves that don't rely on uniqueness before those that do. Have look here http://sudopedia.enjoysudoku.com/Uniqueness_Controversy.html

Leren

Ah, now I understand. It's not that the DP pattern isn't easier to spot, it's that you'd prefer not to use uniqueness for the reasons discussed in the controversy.

[DonM]

SteveG48 wrote: You would spot that before glomming on to a simple DP possible?

I always look for moves that don't rely on uniqueness before those that do. Have look here http://sudopedia.enjoysudoku.com/Uniqueness_Controversy.html
Leren

There is no controversy on this subject anymore. The last vestige of the so-called 'uniqueness' vs. multi-solution puzzles' controvery ended circa 2007-8 (note the date on that sudopedia entry). Sudoku was first introduced as a paper and pencil, fill-in-the-blanks puzzle so whether there could be more than one solution didn't really matter. However, once Sudoku-solving was taken up as a Boolean-logic solving challenge, the assumption of there being one solution/uniqueness became a necessity.

For several years now, it has been assumed that any puzzle we solve using these methods only has only one solution and, likewise, uniqueness is assumed. And, any puzzle that turned out to have more than one solution has been considered faulty. The fact that this issue would even be considered as a reason for the order in which one solves a puzzle indicates how so much of what was learned about Soduku-solving during the period of 2005-2010 is in danger of being lost.

IMO, a better reason for looking for basic chains before uniqueness-based methods is that when it comes to solving, simplicity and elegance go hand-in-hand.

[eleven]

My way is neither type 3 nor 4. It is so easy to see, that no 6 or 7 can be outside the DP cells in columns 12 - except r7c2=7.

Code: Select all

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

[Marty R.]

My way is neither type 3 nor 4. It is so easy to see, that no 6 or 7 can be outside the DP cells in columns 12 - except r7c2=7.

Code: Select all

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

Not looking to start anything here, but is this merely a matter of semantics?

That no 6s can exist is a given because they're an X-Wing. That r7c2=7 is a function of there being just three 7s in c2, two of which cannot exist because of the very definition of a Type 4, i.e., the X-Wing on 6s.

It can also be look upon as an external analysis, but again, r7c2=7 because it's the only external deadly candidate.

[eleven]

Hi Marty,
you are right, in this case with a pair and one of the candidates in an x-wing, Keith's type 4 and external DP view will give exactly the same (if it's not inside then outside).
A third point of view is to see it as "hidden unique rectangle" eliminations.