The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |6.8|.42|.1.|
 |.7.|.3.|4..|
 |2..|1.8|3.6|
 |---+---+---|
 |..5|8..|...|
 |91.|...|...|
 |8.7|..9|..4|
 |---+---+---|
 |.84|...|6.2|
 |3..|...|...|
 |..6|..4|8.3|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 6     3     8      | c57   4     2      | 579   1     579    |
| 5     7     1      | 9     3     6      | 4     2     8      |
| 2     4     9      | 1    d57    8      | 3    e57    6      |
|--------------------+--------------------+--------------------|
| 4     26    5      | 8     127   13     | 179   36    179    |
| 9     1     3      | 4     6     57     | 2     8     57     |
| 8     26    7      | 235   125   9      | 15    36    4      |
|--------------------+--------------------+--------------------|
| 17    8     4      |b37-5  179-5 13     | 6    f579   2      |
| 3     9     2      | 6     8    a57     | 17-5    4   17-5   |
| 17    5     6      |b27    1279  4      | 8     79    3      |
*--------------------------------------------------------------*

W Wing (57) with transport : (5=7) r8c6 - r79c4 = r1c4 - (7=5) r3c5 - r3c8 = (5) r7c8 => - 5 r7c45, r8c79; stte

Leren

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 6     3     8     | 7-5   4     2     |a579   1    a579   |
 | 5     7     1     | 9     3     6     | 4     2     8     |
 | 2     4     9     | 1     57    8     | 3    b57    6     |
 *-------------------+-------------------+-------------------|
 | 4     26    5     | 8     127   13    | 179   36    179   |
 | 9     1     3     | 4     6     57    | 2     8     57    |
 | 8     26    7     |f235   125   9     | 15    36    4     |
 *-------------------+-------------------+-------------------|
 | 17    8     4     |f357   1579  13    | 6    c579   2     |
 | 3     9     2     | 6     8    e57    |d157   4    d157   |
 | 17    5     6     |f27    1279  4     | 8     79    3     |
 *-----------------------------------------------------------*


(5)r1c79 = r3c8 - r7c8 = r8c79 - (5=7)r8c6 - (7=235)r679c4 => -5 r1c4 ; stte

[Marty R.]

Code: Select all

+---------+-------------+-------------+
| 6  3  8 | 57  4    2  | 579 1   579 |
| 5  7  1 | 9   3    6  | 4   2   8   |
| 2  4  9 | 1   57   8  | 3   57  6   |
+---------+-------------+-------------+
| 4  26 5 | 8   127  13 | 179 36  179 |
| 9  1  3 | 4   6    57 | 2   8   57  |
| 8  26 7 | 235 125  9  | 15  36  4   |
+---------+-------------+-------------+
| 17 8  4 | 357 1579 13 | 6   579 2   |
| 3  9  2 | 6   8    57 | 157 4   157 |
| 17 5  6 | 27  1279 4  | 8   79  3   |
+---------+-------------+-------------+


Play this puzzle online at the Daily Sudoku site

DP (79) r14,c79, using externals.

7r1c4=7r4c5=>r3c5<>7

[SteveG48]

Code: Select all

+---------+-------------+-------------+
| 6  3  8 | 57  4    2  | 579 1   579 |
| 5  7  1 | 9   3    6  | 4   2   8   |
| 2  4  9 | 1   57   8  | 3   57  6   |
+---------+-------------+-------------+
| 4  26 5 | 8   127  13 | 179 36  179 |
| 9  1  3 | 4   6    57 | 2   8   57  |
| 8  26 7 | 235 125  9  | 15  36  4   |
+---------+-------------+-------------+
| 17 8  4 | 357 1579 13 | 6   579 2   |
| 3  9  2 | 6   8    57 | 157 4   157 |
| 17 5  6 | 27  1279 4  | 8   79  3   |
+---------+-------------+-------------+


Play this puzzle online at the Daily Sudoku site

DP (79) r14,c79, using externals.

7r1c4=7r4c5=>r3c5<>7

Good one, Marty!

[Sudtyro2]

Code: Select all

+---------+-------------+-------------+
| 6  3  8 | 57  4    2  | 579 1   579 |
| 5  7  1 | 9   3    6  | 4   2   8   |
| 2  4  9 | 1   5-7  8  | 3   57  6   |
+---------+-------------+-------------+
| 4  26 5 | 8   127  13 | 179 36  179 |
| 9  1  3 | 4   6    57 | 2   8   57  |
| 8  26 7 | 235 125  9  | 15  36  4   |
+---------+-------------+-------------+
| 17 8  4 | 357 1579 13 | 6   579 2   |
| 3  9  2 | 6   8    57 | 157 4   157 |
| 17 5  6 | 27  1279 4  | 8   79  3   |
+---------+-------------+-------------+

DP (79) r14,c79, using externals.
7r1c4=7r4c5=>r3c5<>7

Marty, I like your use of potential DPs, but I'll admit to being a little slow on what “using externals” means. Here's my own long way around...and comments are welcomed.

Almost-DP => strong inference: (5)r1c79=(1)r4c79
So, one can work up an AIC using that strong inference:
(7=5)r1c4-(5)r1c79=(1)r4c79-(1=5)r6c7-(5=7)r5c9-(7)r5c6=(7)r4c5 => r3c5<>7

BTW, I recall that (in an AIC) Ron Moore of the old Sudocue Users forum would write that ADP strong inference as:
(5)r1c79=(1)r4c79 => (5=79)r1c79-DP-(79=1)r4c79
But, I never fully understood his notation. Any help on that?

I “think” one can also look at the ADP problem as a 3-element SIS:

Code: Select all

DP                                            => Invalid puzzle
||
(5)r1c79-(5=7)r1c4                            => r3c5<>7
||
(1)r4c79-(1=5)r6c7-(5=7)r5c9-(7)r5c6=(7)r4c5  => r3c5<>7

Note that if we drop the DP element and mirror-image the second element, we reproduce the full AIC shown above. It also appears that one could substitute (5=7)r3c8 for (5=7)r1c4 in the above SIS (and AIC) and still have the same elimination.

So, my interpretation of “externals” is that (before happy-hour) one can just mentally run those two SIS chains without having to construct the full AIC. Is that the right idea?

SteveC

[Marty R.]

Code: Select all

+---------+-------------+-------------+
| 6  3  8 | 57  4    2  | 579 1   579 |
| 5  7  1 | 9   3    6  | 4   2   8   |
| 2  4  9 | 1   5-7  8  | 3   57  6   |
+---------+-------------+-------------+
| 4  26 5 | 8   127  13 | 179 36  179 |
| 9  1  3 | 4   6    57 | 2   8   57  |
| 8  26 7 | 235 125  9  | 15  36  4   |
+---------+-------------+-------------+
| 17 8  4 | 357 1579 13 | 6   579 2   |
| 3  9  2 | 6   8    57 | 157 4   157 |
| 17 5  6 | 27  1279 4  | 8   79  3   |
+---------+-------------+-------------+

SteveC,

In this line of notation you are using internals, that is, to kill the DP there must be one of the non-deadly candidates present, either 1 or 5, in the DP cells.

Almost-DP => strong inference: (5)r1c79=(1)r4c79

When using externals, you are looking for the deadly candidates outside the DP cells, but in the same house, since the presence of a 7 or 9 outside the DP cells also kills the DP. When using externals you can choose to use a box or a line, whatever works best. This is a pretty simple DP where using the externals obviously gives the same result as the internals, but I used externals since that resulted in the shortest possible notation string.

I hope this is clear; if not, hopefully someone will see it and can explain it more clearly.

[ArkieTech]

Almost-DP => strong inference: (5)r1c79=(1)r4c79

When using externals, you are looking for the deadly candidates outside the DP cells, but in the same house, since the presence of a 7 or 9 outside the DP cells also kills the DP. When using externals you can choose to use a box or a line, whatever works best. This is a pretty simple DP where using the externals obviously gives the same result as the internals, but I used externals since that resulted in the shortest possible notation string.

I hope this is clear; if not, hopefully someone will see it and can explain it more clearly.

I like this notation:

(7r1c4=7r4c5)dp:79r14c79 => -7r3c5

[daj95376]

Code: Select all

+---------+-------------+-------------+
| 6  3  8 | 57  4    2  | 579 1   579 |
| 5  7  1 | 9   3    6  | 4   2   8   |
| 2  4  9 | 1   5-7  8  | 3   57  6   |
+---------+-------------+-------------+
| 4  26 5 | 8   127  13 | 179 36  179 |
| 9  1  3 | 4   6    57 | 2   8   57  |
| 8  26 7 | 235 125  9  | 15  36  4   |
+---------+-------------+-------------+
| 17 8  4 | 357 1579 13 | 6   579 2   |
| 3  9  2 | 6   8    57 | 157 4   157 |
| 17 5  6 | 27  1279 4  | 8   79  3   |
+---------+-------------+-------------+

DP (79) r14,c79, using externals.
7r1c4=7r4c5=>r3c5<>7

Marty, I like your use of potential DPs, but I'll admit to being a little slow on what “using externals” means.

In order to prevent a DP, there must be at least one candidate that sees the DP and is one of the DP values. Without explaining all of the possible combinations for external candidates, suffice it to say that 7r1c4 (in [r1]) and 7c4c5 (in [r4]) are an acceptable combination for Marty to select.

Marty's externals are strongly linked through hidden pairs to the (79)DP[r14c79]:

Code: Select all

7r1c4 = hp(79)r1c79 -DP- hp(79)r4c79 = 7r4c5  =>  -7 r3c5


[daj95376]

_

I can't pass up a prime example of:

Code: Select all

 +--------------------------------------------------------------+
 |  6     3     8     | *57    4     2     |  59-7  1     59-7  |
 |  5     7     1     |  9     3     6     |  4     2     8     |
 |  2     4     9     |  1     5-7   8     |  3    *57    6     |
 |--------------------+--------------------+--------------------|
 |  4     26    5     |  8     127   13    |  179   36    179   |
 |  9     1     3     |  4     6     57    |  2     8     57    |
 |  8     26    7     |  235   125   9     |  15    36    4     |
 |--------------------+--------------------+--------------------|
 | *17    8     4     | *357   1579  13    |  6    *579   2     |
 |  3     9     2     |  6     8     57    |  157   4     157   |
 | *17    5     6     | *27    1279  4     |  8    *79    3     |
 +--------------------------------------------------------------+
 # 45 eliminations remain

 *** Swordfish Skyscraper ***

 (7):  r1c4 = X-Wing[c14\r79] - r79c8 = r3c8  =>  -7 r1c79,r3c5


 -aka-

 Sashimi Swordfish c148\r79+1 w/fin cell r3c8  =>  -7 r1c79
 Sashimi Swordfish c148\r79+2 w/fin cell r1c4  =>  -7 r3c5


_

[Luke]

DP (79) r14,c79, using externals.

7r1c4=7r4c5=>r3c5<>7

Nice, Marty! This seems the best way to handle this puzzle. @ Sudtyro2, you might be interested in this very nice treatise and discussion on external inferences by tlanglet.

Sidebar:
A little dismaying to me is how the term "DP" has won the battle for all things deadly. We know the difference between unique rectangles, BUG-Lites, MUGs, et al. So, for the sake of those readers who don't know the difference, I can't see why we aren't calling things what they are.

[Marty R.]

DP (79) r14,c79, using externals.

7r1c4=7r4c5=>r3c5<>7

Nice, Marty! This seems the best way to handle this puzzle. @ Sudtyro2, you might be interested in this very nice treatise and discussion on external inferences by tlanglet.

Sidebar:
A little dismaying to me is how the term "DP" has won the battle for all things deadly. We know the difference between unique rectangles, BUG-Lites, MUGs, et al. So, for the sake of those readers who don't know the difference, I can't see why we aren't calling things what they are.

Luke,

Thank you.

As to the sidebar, I'm probably in the minority, but I don't use the terms BUG-Lite or MUG because they mean nothing, except to the people who know and use them. They must be very confusing to a new player or reader. However, they're all potential deadly patterns, a descriptive, meaningful term to all.

Cheers.

[Luke]

As to the sidebar, I'm probably the one in the minority ...

Actually, I don't think you are, I think I'm in the minority when I wonder why the "DP" reigns while so many other terms are categorized down to the 8th substratum ...

... but I don't use the terms BUG-Lite or MUG because they mean nothing, except to the people who know and use them. They must be very confusing to a new player or reader. However, they're all potential deadly patterns, a descriptive, meaningful term to all..

Then to advocate for the dark side, what about this rhetorical statement:

"I don't use the terms W-wing, H2-wing, L3-wing, S4-wing, m5-wing etc etc etc because they mean nothing, except to the people who know and use them. They must be very confusing to a new player or reader. However, they're all just wings, a descriptive, meaningful term to all."

[daj95376]

Then to advocate for the dark side, what about this rhetorical statement:

"I don't use the terms W-wing, H2-wing, L3-wing, S4-wing, m5-wing etc etc etc because they mean nothing, except to the people who know and use them. They must be very confusing to a new player or reader. However, they're all just wings, a descriptive, meaningful term to all."

My turn to play devil's advocate?

If people know and use terms with confidence, then there's no reason not to use them. However, if people don't feel confident with a term, then they're going to use something else. A DP pattern of cells and candidates is often the common denominator for many of us remaining in the forum. You are comfortable with more elaborate terms. That doesn't help us.

I tend to follow:

Code: Select all

===== ===== ===== ===== ===== ===== Deadly Pattern vs. Unavoidable Set (from RW)

A deadly pattern is not the same as an unavoidable set. A deadly pattern is a set of unsolved cells (and candidates) that has (would force) multiple solutions. An unavoidable set is a set of solved cells that can be rearranged without affecting the rest of the puzzle. Basically, an unavoidable set is a solution to a deadly pattern. Or the other way around, if you remove all digits in an unavoidable set, you get a deadly pattern.

 | ab ab . |         | A B . |
 +---------+         +-------+
 | ab ab . |         | B A . |

Deadly Pattern    Unavoidable Set


(inserted by me)


Note: I don't completely agree with "Or the other way around, if you remove all digits in an unavoidable set, you get a deadly pattern" because other candidates may also become present in the UA cells. However, I understand RW's general point, so I keep the full quote.

When you extend the above DP to include other candidates in these (and other) cells, then you end up with what Keith and Mike Barker document as Unique Rectangle patterns.

What is it when a DP is embedded in a chain -- as I indicated for Marty's usage? It's no longer a UR, is it?

[Edit: dropped question about AUR.]
_

[Marty R.]

Luke, I can't argue with your rhetorical statement, but we were talking about DPs. I don't know of any alternative, descriptive terms for the other techniques.

Danny, I've chided someone for his use of AUR when the pattern is a defined UR, i.e., Type 1, 2, etc. I suppose an AUR is also a potential DP.