The New Sudoku Players' Forum

[eleven]

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

[Luke]

Thanx, eleven, these will be fun/educational.

Code: Select all

*--------------------------------------------------------------------*
 | 8      2      7      | 3      9      4      | 5      6      1      |
 | 169    3      169    | 5      16     2      | 7      8      4      |
 | 5      4      16     | 7      16     8      | 3      2      9      |
 |----------------------+----------------------+----------------------|
 | 4      7      289    |*29     5      6      |*29+8   1      3      |
 | 269   *69     5      | 1      8      3      |*269    4      7      |
 | 3     *69+1   12689  |*29     4      7      |*269+8  5      28     |
 |----------------------+----------------------+----------------------|
 | 269    5      269    | 68     3      1      | 4      7      28     |
 | 7      16     4      | 68     2      9      | 1-8    3      5      |
 | 12     8      3      | 4      7      5      | 12     9      6      |
 *--------------------------------------------------------------------*

(269)MUG band 2
||
(8)r46c7
||
(1)r6c2-r8c2=(1)r8c7
||
(2)r5c7-(2=691)r5c12, r6c2-r8c2=(1)r8c7

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 8     2     7      | 3     9     4      | 5     6     1      |
|*169   3    *169    | 5    *16    2      | 7     8     4      |
| 5     4    *16     | 7    *16    8      | 3     2     9      |
|--------------------+--------------------+--------------------|
| 4     7     28     | 29    5     6      | 289   1     3      |
| 26    69    5      | 1     8     3      | 269   4     7      |
| 3     169   1268   | 29    4     7      | 2689  5     28     |
|--------------------+--------------------+--------------------|
|*69+2  5    *69+2   | 68    3     1      | 4     7     8-2    |
| 7     16    4      | 68    2     9      | 18    3     5      |
| 1-2   8     3      | 4     7     5      | 12    9     6      |
*--------------------------------------------------------------*

7 Cell DP (169+2) r2c135, r3c35, r7c13. Either r7c1 or r7c3 = 2; => - 2 r7c9, r9c1; stte

Leren

[eleven]

[Edit:] cross posted
@Luke: Great, you also found an alternative uniqueness solution
@Leren: That was, what i had in mind.
btw others are welcome.

[Luke]

Code: Select all

*--------------------------------------------------------------*
| 8     2     7      | 3     9     4      | 5     6     1      |
|*69+1  3    *169    | 5    *16    2      | 7     8     4      |
| 5     4    *16     | 7    *16    8      | 3     2     9      |
|--------------------+--------------------+--------------------|
| 4     7     28     | 29    5     6      | 289   1     3      |
| 26    69    5      | 1     8     3      | 269   4     7      |
| 3     169   1268   | 29    4     7      | 2689  5     28     |
|--------------------+--------------------+--------------------|
|*69+2  5    *69+2   | 68    3     1      | 4     7     28     |
| 7     16    4      | 68    2     9      | 18    3     5      |
| 12    8     3      | 4     7     5      | 12    9     6      |
*--------------------------------------------------------------*

Until this series, if I had seen this pattern I'd have worked the (1)=(2) link (overlapping URs) without realizing the +1 could be included in the pattern. In fact, that's exactly what I did

Proving the (1)r2c1 is part of a MUG pattern is not difficult. All possible arrangements force URs or a no solution state.

[eleven]

At second glance (thanks Luke) here you can also look at the externals.
There is only one (in the boxes): r8c2=6.

[ronk]

Code: Select all

*--------------------------------------------------------------*
| 8     2     7      | 3     9     4      | 5     6     1      |
|*69+1  3    *169    | 5    *16    2      | 7     8     4      |
| 5     4    *16     | 7    *16    8      | 3     2     9      |
|--------------------+--------------------+--------------------|
| 4     7     28     | 29    5     6      | 289   1     3      |
| 26    69    5      | 1     8     3      | 269   4     7      |
| 3     169   1268   | 29    4     7      | 2689  5     28     |
|--------------------+--------------------+--------------------|
|*69+2  5    *69+2   | 68    3     1      | 4     7     28     |
| 7     16    4      | 68    2     9      | 18    3     5      |
| 12    8     3      | 4     7     5      | 12    9     6      |
*--------------------------------------------------------------*

Until this series, if I had seen this pattern I'd have worked the (1)=(2) link (overlapping URs) without realizing the +1 could be included in the pattern. In fact, that's exactly what I did ...

Proving the (1)r2c1 is part of a MUG pattern is not difficult. All possible arrangements force URs or a no solution state.

By saying that 1r2c1 is part of the uniqueness pattern, I think you are breaking the direct connection between Uniqueness Patterns in the solvers' world and UnAvoidable Sets in the puzzle makers' world. Moreover inclusion of 1r2c1 causes XSUDO to say the pattern is not a MUG (pMUG actually).

There is a subtle definition change going on here, and it apparently is due to the treatment of "no solution states."

[Luke]

There is a subtle definition change going on here, and it apparently is due to the treatment of "no solution states."

Thanks for your insight, Ronk. By "definition" I imagine you are referencing the one that includes the idea that all MUGs should break down into BUG-Lites. This pattern does not follow that definition in its current state.

Am I correct in assuming that you do not consider the pattern a reduction of the four-candidate L-shaped MUG prototype that's being studied in this series?

The pattern is "impossible" with (1) in r2c1 because there won't be enough candidates to go around. Isn't that enough to consider it deadly?

[ronk]

Am I correct in assuming that you do not consider the pattern a reduction of the four-candidate L-shaped MUG prototype that's being studied in this series?

Correct, [edit: but only because of the 1r2c1 candidate.]

The pattern is "impossible" with (1) in r2c1 because there won't be enough candidates to go around. Isn't that enough to consider it deadly?

Deadly in the general sense, yes. But I use the Deadly Pattern (DP) term as a collective for UR, BUG, BUG-Lite and MUG (and did I miss anything?) It has not included impossible patterns and "no solutions." I think it would be a mistake for me to try to change that now. I confuse myself too easily as it is.

[Luke]

Am I correct in assuming that you do not consider the pattern a reduction of the four-candidate L-shaped MUG prototype that's being studied in this series?

Correct, [edit: but only because of the 1r2c1 candidate.]

How about at givens, is this a MUG? (aMUG,pMUG)

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 *-----------*
 |8.7|3.4|.61|
 |.3.|5.2|78.|
 |.4.|7.8|...|
 |---+---+---|
 |4..|..6|..3|
 |..5|183|.47|
 |...|...|...|
 |---+---+---|
 |.5.|...|4..|
 |7.4|.29|.3.|
 |.83|.7.|.96|
 *-----------*

 
 *-----------------------------------------------------------------------------*
 | 8       29      7       | 3       9       4       | 259     6       1       |
 |*169     3      *169     | 5      *169     2       | 7       8       49      |
 |*1269+5  4      *1269    | 7      *169     8       | 2359    25      259     |
 |-------------------------+-------------------------+-------------------------|
 | 4       1279    1289    | 29      59      6       | 12589   125     3       |
 | 269     269     5       | 1       8       3       | 269     4       7       |
 | 12369   12679   12689   | 249     459     57      | 125689  125     2589    |
 |-------------------------+-------------------------+-------------------------|
 |*1269    5      *1269    | 68      136     1       | 4       127     28      |
 | 7       16      4       | 68      2       9       | 158     3       58      |
 | 12      8       3       | 4       7       15      | 125     9       6       |
 *-----------------------------------------------------------------------------*

[blue]

But I use the Deadly Pattern (DP) term as a collective for UR, BUG, BUG-Lite and MUG (and did I miss anything?) It has not included impossible patterns and "no solutions."

Hi ronk,

I do understand what you're driving at.

Technically, though, BUG patterns in "unique" puzzles, have never had solutions.
The same can't always be said for BUG-Lite patterns, but it's seems likely that they haven't always had solutions.

Maybe what you're really objecting to (if that isn't "too strong"), is the idea of a MUG that doesn't satisfy the property that [ it has solutions in the first place, and then ] each of its candidates is part of at least one of its solutions ?

Hairy MUGs -vs- clean shaven

[ronk]

How about at givens, is this a MUG? (aMUG,pMUG)

Code: Select all

 *-----------------------------------------------------------------------------*
 | 8       29      7       | 3       9       4       | 259     6       1       |
 |*169     3      *169     | 5      *169     2       | 7       8       49      |
 |*1269+5  4      *1269    | 7      *169     8       | 2359    25      259     |
 |-------------------------+-------------------------+-------------------------|
 | 4       1279    1289    | 29      59      6       | 12589   125     3       |
 | 269     269     5       | 1       8       3       | 269     4       7       |
 | 12369   12679   12689   | 249     459     57      | 125689  125     2589    |
 |-------------------------+-------------------------+-------------------------|
 |*1269    5      *1269    | 68      136     1       | 4       127     28      |
 | 7       16      4       | 68      2       9       | 158     3       58      |
 | 12      8       3       | 4       7       15      | 125     9       6       |
 *-----------------------------------------------------------------------------*

There is no contradiction between the pencilmarks and this "fully-populated" permeable MUG (pMUG).

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 .       .       .       | .       .
 1269    .       1269    | .       1269
 1269    .       1269    | .       1269
-------------------------+------------
 .       .       .       | .       .
 .       .       .       | .       .
 .       .       .       | .       .
-------------------------+------------
 1269    .       1269    | .       .
 .       .       .       | .       .
 .       .       .       | .       .

This 8-cell BUG-Lite e.g. is still possible, so the pencilmark "parent" above is still a pMUG.

Code: Select all

 .       .       .       | .       .
 69      .       19      | .       16
 26      .       12      | .       16
-------------------------+------------
 .       .       .       | .       .
 .       .       .       | .       .
 .       .       .       | .       .
-------------------------+------------
 29      .       29      | .       .
 .       .       .       | .       .
 .       .       .       | .       .

[ronk]

But I use the Deadly Pattern (DP) term as a collective for UR, BUG, BUG-Lite and MUG (and did I miss anything?) It has not included impossible patterns and "no solutions."

Technically, though, BUG patterns in "unique" puzzles, have never had solutions.
The same can't always be said for BUG-Lite patterns, but it's seems likely that they haven't always had solutions.

Don't know about Luke's usage for sure but my "no solution" here is as an alias for impossible solution.

Maybe what you're really objecting to (if that isn't "too strong"), is the idea of a MUG that doesn't satisfy the property that [ it has solutions in the first place, and then ] each of its candidates is part of at least one of its solutions ?

Hairy MUGs -vs- clean shaven

LOL, but I do think every candidate of a fully-populated permeable MUG must be a member of at least one possible fully-permeated DP.

[Luke]

Cool stuff!

The "Muggy" puzzle series was offered up as a "Find The MUG" challenge. I did not recognize the Muggy 6 pattern as a MUG, so when it was revealed as the correct solution I applied one of my personal MUG-proving methods to it. Some variations resulted in the pattern having no solutions. That is all I meant by the term.

I've done this before without raising objections, like with this MUG.

I am aware that certain patterns are impossible without relying on uniqueness, like broken wings or oddagons. If this pattern is not a MUG but an impossible, that's fine with me!

In fact, it's very interesting to become aware of a new impossible pattern that has to my knowledge never been specifically ID'd before....if that indeed is what's happening here.

I'd be interested in what eleven has to say...

[eleven]

I'd be interested in what eleven has to say...

Hm, i like the pattern, and i call it MUG like Myth, who has found it.
And i like the combination of "impossible" and "uniqueness" arguments.