The New Sudoku Players' Forum

[ArkieTech]

From my collection. Source unknown.

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 *-----------*
 |7..|8.6|4..|
 |...|2..|...|
 |...|...|.3.|
 |---+---+---|
 |1..|...|..2|
 |...|5..|8..|
 |93.|...|...|
 |---+---+---|
 |.28|...|...|
 |...|.9.|.1.|
 |...|.3.|...|
 *-----------*


Play/Print this puzzle online

[pjb]

I went for the BUG-lite of 67's first: r2c89, r4c78, r9c79 => -4 r6c9, r7c8; giving:

Code: Select all

7      9      3      | 8      5      6      | 4      2      1     
8      5      14     | 2      14     3      | 9      67     67     
2      46     146    | 9      147    47     | 5      3      8     
---------------------+----------------------+---------------------
1      8      5      | 3     a67     9      |b67     4      2     
46     467    467    | 5      2      1      | 8      9      3     
9      3      2      | 467    8      47     | 1      5      67     
---------------------+----------------------+---------------------
46     2      8      | 1      47-6   5      | 3     d67     9     
3      467    467    | 46     9      8      | 2      1      5     
5      1      9      | 67     3      2      |c67     8      4     


(6=7) r4c5 - (7=6) r4c7 - (6=7) r9c7 - (7=6) r7c8 => -6 r7c5; stte

Phil

[Luke]

Hey, check this out, just for the hellavit. Because this puzzle is not *too* awful difficult, is anyone down for an added challenge?

Code: Select all

 *--------------------------------------------------*
 | 7    9    3    | 8    5    6    | 4    2    1    |
 | 8    5    14   | 2    14   3    | 9    67   67   |
 | 2    46   146  | 9    147  47   | 5    3    8    |
 |----------------+----------------+----------------|
 | 1    8    5    | 3    467  9    | 67   467  2    |
 | 46   467  467  | 5    2    1    | 8    9    3    |
 | 9    3    2    | 467  8    47   | 1    5    467  |
 |----------------+----------------+----------------|
 | 46   2    8    | 1    467  5    | 3    467  9    |
 | 3    467  467  | 46   9    8    | 2    1    5    |
 | 5    1    9    | 467  3    2    | 67   8    467  |
 *--------------------------------------------------*

This grid has more than one Type 1 deadly pattern. Find the one that reduces it to singles...

[daj95376]

Code: Select all

 after basics
 +-----------------------------------------------------+
 |  7    9    3    |  8    5    6    |  4    2    1    |
 |  8    5    14   |  2    14   3    |  9   *67  *67   |
 |  2    46   146  |  9    147  47   |  5    3    8    |
 |-----------------+-----------------+-----------------|
 |  1    8    5    |  3   *67+4 9    | *67   467  2    |
 |  46   467  467  |  5    2    1    |  8    9    3    |
 |  9    3    2    | *67+4 8    47   |  1    5   *67+4 |
 |-----------------+-----------------+-----------------|
 |  46   2    8    |  1   *67+4 5    |  3   *67+4 9    |
 |  3    467  467  |  46   9    8    |  2    1    5    |
 |  5    1    9    | *67+4 3    2    | *67   8    467  |
 +-----------------------------------------------------+
 # 40 eliminations remain


While searching for Luke's DP, I found <67> in the (*) cells. Anything that forces this pattern must be false.

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4r6c6, 4r4c8, 4r9c9, 4r8c4; <67> DP  =>  r6c6<>4


A network using memory on eliminations for <4>:

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(7=14)r23c5 - (4)r47c5,r3c6 = r6c6 - r6c49 = r4c8 - r7c8 = r9c9 - r9c4; <67> DP  =>  r3c5=7


[Leren]

Can't see a single DP move. (467) DP r358c23 => r3c3 <> 4,6 followed by an Avoidable Rectangle (14) r23c35 => r3c5 <> 4; stte

Leren

[Luke]

Can't see a single DP move.

Thanks for looking, Leren, but I think you did find the pattern. When DPs overlap like this they become a single pattern. They don't have to be the same type, any DPs can be mixed and matched. If that's too broad a statement, I'm open to discussion.

In this case the potential (467)MUG overlaps with the (14)AUR, creating a Muggur, shall we say.

Code: Select all

*--------------------------------------------------*
 | 7    9    3    | 8    5    6    | 4    2    1    |
 | 8    5   *14   | 2   *14   3    | 9    67   67   |
 | 2   *46  *146  | 9   *14+7 47   | 5    3    8    |
 |----------------+----------------+----------------|
 | 1    8    5    | 3    467  9    | 67   467  2    |
 | 46  *467 *467  | 5    2    1    | 8    9    3    |
 | 9    3    2    | 467  8    47   | 1    5    467  |
 |----------------+----------------+----------------|
 | 46   2    8    | 1    467  5    | 3    467  9    |
 | 3   *467 *467  | 46   9    8    | 2    1    5    |
 | 5    1    9    | 467  3    2    | 67   8    467  |
 *--------------------------------------------------*

The only out is 7(r3c5), and there's the Type 1 DP. Overlapping patterns can be more densely hidden, but still available for the strong inference sets that we commonly use for more conventional DPs. Why not, eh?

[tlanglet]

Luke,

I just looked at the puzzle for today and could not help but read all the posts after noting that you contributed. I doubt that I would have found the overlapping DPs in any case.

One comment. You solution is a Type 1 DP, r3c5=7, which is the "internal" strong inference. The only "external" strong inference is r3c6=4.

Ted

[Marty R.]

Code: Select all

+------------+------------+------------+
| 7  9   3   | 8   5   6  | 4  2   1   |
| 8  5   14  | 2   14  3  | 9  67  67  |
| 2  46  146 | 9   147 47 | 5  3   8   |
+------------+------------+------------+
| 1  8   5   | 3   467 9  | 67 467 2   |
| 46 467 467 | 5   2   1  | 8  9   3   |
| 9  3   2   | 467 8   47 | 1  5   467 |
+------------+------------+------------+
| 46 2   8   | 1   467 5  | 3  467 9   |
| 3  467 467 | 46  9   8  | 2  1   5   |
| 5  1   9   | 467 3   2  | 67 8   467 |
+------------+------------+------------+


I couldn't find the one-stepper. Too many 467s for me to process.

DP (67)r249c789 4r4c8=4r9c9=>r6c9,r7c8<>4

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+------------+------------+----------+
| 7  9   3   | 8   5   6  | 4  2  1  |
| 8  5   14  | 2   14  3  | 9  67 67 |
| 2  46  146 | 9   147 47 | 5  3  8  |
+------------+------------+----------+
| 1  8   5   | 3   67  9  | 67 4  2  |
| 46 467 467 | 5   2   1  | 8  9  3  |
| 9  3   2   | 467 8   47 | 1  5  67 |
+------------+------------+----------+
| 46 2   8   | 1   467 5  | 3  67 9  |
| 3  467 467 | 46  9   8  | 2  1  5  |
| 5  1   9   | 67  3   2  | 67 8  4  |
+------------+------------+----------+


Remote Pairs r9c4=67-r9c7=r4c7-r6c9=>r6c4<>67

[daj95376]

Marty, my solver didn't find a single-stepper. However, I did notice that my previous solution could be shortened.

Code: Select all

 after basics
 +-----------------------------------------------------+
 |  7    9    3    |  8    5    6    |  4    2    1    |
 |  8    5    14   |  2    14   3    |  9    67   67   |
 |  2    46   146  |  9    147  47   |  5    3    8    |
 |-----------------+-----------------+-----------------|
 |  1    8    5    |  3    467  9    | *67   467  2    |
 |  46   467  467  |  5    2    1    |  8    9    3    |
 |  9    3    2    | *67+4 8    47   |  1    5   *67+4 |
 |-----------------+-----------------+-----------------|
 |  46   2    8    |  1    467  5    |  3    467  9    |
 |  3    467  467  |  46   9    8    |  2    1    5    |
 |  5    1    9    | *67+4 3    2    | *67   8    467  |
 +-----------------------------------------------------+
 # 40 eliminations remain


A <67> oddagon in the (*) cells. Anything that forces this pattern must be false.

Code: Select all

(4): r8c4 - r69c4 = r9c9 - r6c9; <67> oddagon  =>  r8c4<>4


[ArkieTech]

Code: Select all

 *--------------------------------------------------*
 | 7    9    3    | 8    5    6    | 4    2    1    |
 | 8    5    14   | 2    14   3    | 9   *67  *67   |
 | 2    46   146  | 9    147  47   | 5    3    8    |
 |----------------+----------------+----------------|
 | 1    8    5    | 3    67-4 9    |*67  *4-67 2    |
 | 46   467  467  | 5    2    1    | 8    9    3    |
 | 9    3    2    | 467  8    47   | 1    5    467  |
 |----------------+----------------+----------------|
 | 46   2    8    | 1    4-67 5    | 3    467  9    |
 | 3    467  467  | 46   9    8    | 2    1    5    |
 | 5    1    9    | 467  3    2    |*67   8   *4-67 |
 *--------------------------------------------------*
bug lite *
=> -67r4c8,r7c5,r9c9 -4r6c9,r7c8; ste


[Leren]

My default solving order found a Type 4 UR (14) r23c35 => r2c35 <> 4 followed immediately by the (467) DP r358c23 => r3c3 <> 6; stte

As there were no intervening eliminations between these 2 moves you might be able to claim that they are a single combined move ... maybe.

ArkieTech Wrote: bug lite * => -67r4c8,r7c5,r9c9 -4r6c9,r7c8; ste

Perhaps I don't understand enough about bug lites but the only direct elimination I can see from your 6 cell pattern is r6c9 <> 4 => r4c8, r9c9 <> 67, r4c5, r7c8, r9c4 <> 4. I can't see r7c5 <> 67. Could you explain ?

Leren

[ArkieTech]

I can't see r7c5 <> 67. Could you explain ?

To break the 67 dp either 4r4c8 or 4r9c9 is needed. This results in r7c5 seeing two cells containing 67 extensions from the dp r7c8,r4c5 => -67r7c5 (a 16 skyscraper)

Hope this helps

[pjb]

Leren wrote:

My default solving order found a Type 4 UR (14) r23c35 => r2c35 <> 4 followed immediately by the (467) DP r358c23 => r3c3 <> 6; stte

By executing the Type 4 UR first, doesn't the removal of the 4 at r3c3 kill the MUG at r358c23?

ArkiTech wrote:

To break the 67 dp either 4r4c8 or 4r9c9 is needed. This results in r7c5 seeing two cells containing 67 extensions from the dp r7c8,r4c5 => -67r7c5 (a 16 skyscraper)

Using the Type 2 BUG-lite leads to the state in my post above. A skyscraper of 6 and then 7 removes 67 from r7c5, but isn't this a discrete second step rather than part of the BUG-lite?

Phil

[Leren]

pjb wrote: By executing the Type 4 UR first, doesn't the removal of the 4 at r3c3 kill the MUG at r358c23?

I don't see why it should ? The only requirement for the DP is that the six cells can't solve to just 3 digits 467 (with none of them being a given) and this must happen if
r3c3 = 6 so out it goes. In fact you could remove up to 8 candidates from r58c23 (without solving any of them) and the DP would still apply.

Leren