Hi

I need help to get the next step of this puzzle.

10 posts
• Page **1** of **1**

Hi Jacky, the shortest solution I can find is relatively advanced given that only a handful of cells are unsolved. Anyway here goes the explanation.

(1=4) r7c3 - r7c8 = (4-9) r8c8 = (9-1) r8c6 = (1) r8c9 => - 1 r7c9; stte

The gobbledegook below the diagram is an AIC, which is short for Alternating Inference Chain. It shows that at least one of r7c2 or r8c9 must be 1. Since r7c9 can see both of these cells it can't be 1.

The notation stte means Singles to the End, which is a Sudoku Tragic's howl of triumph (Yee Haaah or some such), because the puzzle solves completely after the solver's brilliant (according to them) move with just a cascade of singles.

Anyway I'll explain the AIC in words in case you are unfamiliar with the AIC notation.

Follow the cells in the diagram in the sequence a-b-c-d-e.

Suppose r7c3 was not 1. Then it must be 4. So r7c8 can't be 4. Since there are only two 4's in Column 8, r8c8 must be 4 and therefore not 9. Since there are only two 9's in Row 8, r8c6 must be 9 and therefore not 1.

Finally, since there are only two 1's in Row 8 r8c9 must therefore be 1.

You can reverse the argument and start by assuming that r8c9 was not 1, and following the cells in the reverse order e-d-c-b-a you would conclude that r7c3 was 1.

What all this proves is that r7c3 and r8c9 cannot be both not 1. So you can remove 1 from r7c9 and the puzzle solves with a cascade of singles from there (Yee Haaah !).

For the benefit of others here is Jacky's puzzle status in line format : 645182937293657814817493.5.128974365459236178736815429.6.7285..5823..7...7.5...8.

Leren

- Code: Select all
`*-----------------------------------------------------*`

| 6 4 5 | 1 8 2 | 9 3 7 |

| 2 9 3 | 6 5 7 | 8 1 4 |

| 8 1 7 | 4 9 3 | 26 5 26 |

|-----------------+-----------------+-----------------|

| 1 2 8 | 9 7 4 | 3 6 5 |

| 4 5 9 | 2 3 6 | 1 7 8 |

| 7 3 6 | 8 1 5 | 4 2 9 |

|-----------------+-----------------+-----------------|

| 39 6 a14 | 7 2 8 | 5 b49 3-1 |

| 5 8 2 | 3 d46 19 | 7 c49 e16 |

| 39 7 14 | 5 46 19 | 26 8 1236 |

*-----------------------------------------------------*

(1=4) r7c3 - r7c8 = (4-9) r8c8 = (9-1) r8c6 = (1) r8c9 => - 1 r7c9; stte

The gobbledegook below the diagram is an AIC, which is short for Alternating Inference Chain. It shows that at least one of r7c2 or r8c9 must be 1. Since r7c9 can see both of these cells it can't be 1.

The notation stte means Singles to the End, which is a Sudoku Tragic's howl of triumph (Yee Haaah or some such), because the puzzle solves completely after the solver's brilliant (according to them) move with just a cascade of singles.

Anyway I'll explain the AIC in words in case you are unfamiliar with the AIC notation.

Follow the cells in the diagram in the sequence a-b-c-d-e.

Suppose r7c3 was not 1. Then it must be 4. So r7c8 can't be 4. Since there are only two 4's in Column 8, r8c8 must be 4 and therefore not 9. Since there are only two 9's in Row 8, r8c6 must be 9 and therefore not 1.

Finally, since there are only two 1's in Row 8 r8c9 must therefore be 1.

You can reverse the argument and start by assuming that r8c9 was not 1, and following the cells in the reverse order e-d-c-b-a you would conclude that r7c3 was 1.

What all this proves is that r7c3 and r8c9 cannot be both not 1. So you can remove 1 from r7c9 and the puzzle solves with a cascade of singles from there (Yee Haaah !).

For the benefit of others here is Jacky's puzzle status in line format : 645182937293657814817493.5.128974365459236178736815429.6.7285..5823..7...7.5...8.

Leren

- Leren
**Posts:**2796**Joined:**03 June 2012

Leren wrote:Hi Jacky, the shortest solution I can find is relatively advanced given that only a handful of cells are unsolved. Anyway here goes the explanation.

- Code: Select all
`*-----------------------------------------------------*`

| 6 4 5 | 1 8 2 | 9 3 7 |

| 2 9 3 | 6 5 7 | 8 1 4 |

| 8 1 7 | 4 9 3 | 26 5 26 |

|-----------------+-----------------+-----------------|

| 1 2 8 | 9 7 4 | 3 6 5 |

| 4 5 9 | 2 3 6 | 1 7 8 |

| 7 3 6 | 8 1 5 | 4 2 9 |

|-----------------+-----------------+-----------------|

| 39 6 a14 | 7 2 8 | 5 b49 3-1 |

| 5 8 2 | 3 d46 19 | 7 c49 e16 |

| 39 7 14 | 5 46 19 | 26 8 1236 |

*-----------------------------------------------------*

(1=4) r7c3 - r7c8 = (4-9) r8c8 = (9-1) r8c6 = (1) r8c9 => - 1 r7c9; stte

Leren

Hi leren,

having a look to your PM, I would use the UR r39c79 giving r9c9 13 then the naked pair 13 in r79c9 => 6r8c9 and stte

- champagne
- 2017 Supporter
**Posts:**5586**Joined:**02 August 2007**Location:**France Brittany

I see that Champagne has spotted an easier way. There is a Type 1 UR (26) in the four cells I've marked * in this diagram.

You can remove 26 from r9c9, and the puzzle solves with singles as before. Champagne's suggestion of the naked pair is not actually necessary, as the simplest next move is r3c9 = 2 (only 2 in Column 9).

If you are not familiar with URs let me know and I'll explain further.

Leren

- Code: Select all
`*--------------------------------------------------------------*`

| 6 4 5 | 1 8 2 | 9 3 7 |

| 2 9 3 | 6 5 7 | 8 1 4 |

| 8 1 7 | 4 9 3 |*26 5 *26 |

|--------------------+--------------------+--------------------|

| 1 2 8 | 9 7 4 | 3 6 5 |

| 4 5 9 | 2 3 6 | 1 7 8 |

| 7 3 6 | 8 1 5 | 4 2 9 |

|--------------------+--------------------+--------------------|

| 39 6 14 | 7 2 8 | 5 49 13 |

| 5 8 2 | 3 46 19 | 7 49 16 |

| 39 7 14 | 5 46 19 |*26 8 *13-26 |

*--------------------------------------------------------------*

You can remove 26 from r9c9, and the puzzle solves with singles as before. Champagne's suggestion of the naked pair is not actually necessary, as the simplest next move is r3c9 = 2 (only 2 in Column 9).

If you are not familiar with URs let me know and I'll explain further.

Leren

- Leren
**Posts:**2796**Joined:**03 June 2012

Hi Jacky, I've just noticed that in your puzzle status you have eliminated 1 and 6 from r9c9.

Since the solution has 1 in r9c9 you have made a mistake somewhere, but all of your solved cells can be thought of as clues to a puzzle that has a unique solution. For the record here it is :

Leren

Since the solution has 1 in r9c9 you have made a mistake somewhere, but all of your solved cells can be thought of as clues to a puzzle that has a unique solution. For the record here it is :

- Code: Select all
`*--------------------------*`

| 6 4 5 | 1 8 2 | 9 3 7 |

| 2 9 3 | 6 5 7 | 8 1 4 |

| 8 1 7 | 4 9 3 | 6 5 2 |

|--------+--------+--------|

| 1 2 8 | 9 7 4 | 3 6 5 |

| 4 5 9 | 2 3 6 | 1 7 8 |

| 7 3 6 | 8 1 5 | 4 2 9 |

|--------+--------+--------|

| 9 6 1 | 7 2 8 | 5 4 3 |

| 5 8 2 | 3 4 1 | 7 9 6 |

| 3 7 4 | 5 6 9 | 2 8 1 |

*--------------------------*

Leren

- Leren
**Posts:**2796**Joined:**03 June 2012

I'm actually quite confused by all the short hand, since I'm just new to the forum entirely xD.

So I didn't understand the "gobbledegook" as you mentioned. But I could follow the "summary" and that you could solve them in "singles" easily afterward. Essentially, since these are all pairings, I could follow through "if this is 4 then this blah blah blah" and follow through to see okay that doesn't work out. That just doesn't give that professional feel D;

I do not know what "UR" is, but I used the "skyscraper" or sort method you've told me about long before and eliminated 1 from R9C9 and apparently I also eliminated 6 from R9C9... What's a Type 1 UR ?

How do I read this part : " I would use the UR r39c79 giving r9c9 13 then the naked pair 13 in r79c9 => 6r8c9 "

So I didn't understand the "gobbledegook" as you mentioned. But I could follow the "summary" and that you could solve them in "singles" easily afterward. Essentially, since these are all pairings, I could follow through "if this is 4 then this blah blah blah" and follow through to see okay that doesn't work out. That just doesn't give that professional feel D;

I do not know what "UR" is, but I used the "skyscraper" or sort method you've told me about long before and eliminated 1 from R9C9 and apparently I also eliminated 6 from R9C9... What's a Type 1 UR ?

How do I read this part : " I would use the UR r39c79 giving r9c9 13 then the naked pair 13 in r79c9 => 6r8c9 "

- Jacky
**Posts:**9**Joined:**18 June 2016

Hi Jacky,

UR's, or Unique Rectangles is a big topic. The best thing I can do at this stage is to point you to a couple of good teaching sites that discuss this topic here and here.

Also, you might be interested in reading about the so-called controversy that surrounds uniqueness moves here.

I think I answered your last question in my second post.

Leren

UR's, or Unique Rectangles is a big topic. The best thing I can do at this stage is to point you to a couple of good teaching sites that discuss this topic here and here.

Also, you might be interested in reading about the so-called controversy that surrounds uniqueness moves here.

I think I answered your last question in my second post.

Leren

- Leren
**Posts:**2796**Joined:**03 June 2012

Hi Leren,

I read the articles. It's quite interesting, it's just based on the assumption whether or not this Sudoku has a unique solution for these deadly rectangles or URs. I was just wondering why the skyscraper method proves to be invalid when removing the 1 from R9C9 or am I just not using it correctly... (I probably did the same thing removing 6)

I read the articles. It's quite interesting, it's just based on the assumption whether or not this Sudoku has a unique solution for these deadly rectangles or URs. I was just wondering why the skyscraper method proves to be invalid when removing the 1 from R9C9 or am I just not using it correctly... (I probably did the same thing removing 6)

- Jacky
**Posts:**9**Joined:**18 June 2016

I could recognize skyscraper, and I could use it correctly, but I assumed and overextended it's use into an incorrect field. And I'm stuck again with a new Sudoku problem. I'll come around to uploading it...

Thanks guys!

Thanks guys!

- Jacky
**Posts:**9**Joined:**18 June 2016

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