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immpy
Joined: 06 May 2017
Posts: 571
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 Posted: Sat Jul 22, 2017 4:09 pm Post subject: VH+072217 |
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Enjoy the puzzle.....
| Code: |
+-------+-------+-------+
| . . . | . . . | . 7 9 |
| . . . | . 3 . | 8 . 5 |
| . . . | 8 . 5 | . . 2 |
+-------+-------+-------+
| 5 1 . | 7 . . | . 9 8 |
| . . . | . . . | . . . |
| 4 7 . | . . 2 | . 3 6 |
+-------+-------+-------+
| 8 . . | 9 . 6 | . . . |
| 1 . 6 | . 2 . | . . . |
| 3 5 . | . . . | . . . |
+-------+-------+-------+
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Play this puzzle online at the Daily Sudoku site |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Sat Jul 22, 2017 5:43 pm Post subject: |
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{5C58} -> -{5r8c47, 5r7c7}
| Code: | +------------------+---------------------+---------------------+
| 26 8 5 | 26 14 14 | 3 7 9 |
| 2679 2469 1249 | 26 3 79 | 8 146 5 |
| 679 3469 1349 | 8 79 5 | 146 146 2 |
+------------------+---------------------+---------------------+
| 5 1 23 | 7 6 34 | 24 9 8 |
| 269 2369 2389 | 134 14589 13489 | 1247 1245 147 |
| 4 7 89 | (15) 89 2 | 5(1) 3 6 |
+------------------+---------------------+---------------------+
| 8 24 7 | 9 4(15) 6 | 24(1) -24(15) 3 |
| 1 49 6 | 34(5) 2 347 | 4579 8 47 |
| 3 5 29 | 14 1478 1478 | 269 26 147 |
+------------------+---------------------+---------------------+
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{5R7, 1R76, 5C4} -> -{(24)r7c8}; {2R47} -> -{2r5c2, 2r9c3}; stte |
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ZeroAssoluto
Joined: 05 Feb 2017
Posts: 943
Location: Rimini, Italy
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| Posted: Sat Jul 22, 2017 7:56 pm Post subject: |
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Hi everyone,
after basic
| Code: |
+---------------+------------------+----------------+
| 26 8 5 | 26 14 14 | 3 7 9 |
| 2679 269 14 | 26 3 79 | 8 14 5 |
| 679 3 14 | 8 79 5 | 146 146 2 |
+---------------+------------------+----------------+
| 5 1 23 | 7 6 34 | 24 9 8 |
| 269 269 2389 | 1345 14589 13489 | 12457 1245 147 |
| 4 7 89 | 15 89 2 | 15 3 6 |
+---------------+------------------+----------------+
| 8 24 7 | 9 145 6 | 1245 1245 3 |
| 1 49 6 | 345 2 347 | 4579 8 47 |
| 3 5 29 | 14 1478 1478 | 269 26 147 |
+---------------+------------------+----------------+
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Play this puzzle online at the Daily Sudoku site
Unique rectangle with 1,4 in r23c38 and r3c8=6
Ciao Gianni |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Sat Jul 22, 2017 8:51 pm Post subject: |
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| ZeroAssoluto wrote: | | Unique rectangle with 1,4 in r23c38 and r3c8=6 |
How to prove UR(14)r23c38 -> 0 solution ? |
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ZeroAssoluto
Joined: 05 Feb 2017
Posts: 943
Location: Rimini, Italy
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| Posted: Sat Jul 22, 2017 9:48 pm Post subject: |
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Hi JC,
I'm not trying to prove he has no solutions: or has one or more than one
If the schema has only one solution, can not present a situation with the same pairs of numbers at the 4 vertices of the rectangle;
| Code: |
+---------------+------------------+----------------+
| 26 8 5 | 26 14 14 | 3 7 9 |
| 2679 269 14 | 26 3 79 | 8 14 5 |
| 679 3 14 | 8 79 5 | 146 14 2 |
+---------------+------------------+----------------+
| 5 1 23 | 7 6 34 | 24 9 8 |
| 269 269 2389 | 1345 14589 13489 | 12457 1245 147 |
| 4 7 89 | 15 89 2 | 15 3 6 |
+---------------+------------------+----------------+
| 8 24 7 | 9 145 6 | 1245 1245 3 |
| 1 49 6 | 345 2 347 | 4579 8 47 |
| 3 5 29 | 14 1478 1478 | 269 26 147 |
+---------------+------------------+----------------+
|
Play this puzzle online at the Daily Sudoku site
Otherwise there would be a loop with two possible solutions.
So if the schema has only one solution in r3c8 there can be no number 1 or number 4
I hope I've been able to explain, otherwise we resound
Ciao Gianni |
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ZeroAssoluto
Joined: 05 Feb 2017
Posts: 943
Location: Rimini, Italy
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| Posted: Sat Jul 22, 2017 9:53 pm Post subject: |
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It's not a real technique, but almost a trick you can use when you're sure that the schema has only one solution.
Ciao Gianni |
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immpy
Joined: 06 May 2017
Posts: 571
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| Posted: Sun Jul 23, 2017 8:53 am Post subject: |
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I'm going to defend the Unique Rectangle as a solving technique, based on the fact that a TRUE Sudoku (which I understand roughly translates as "place one number") puzzle has only one possible solution. We can use this fact to help us in our solving. Why not? We eliminate candidates in rows columns and boxes based on the fact that a number can only appear one time in each respective area.
And the Unique Rectangle technique has more than one way of appearing. I am aware of six, depending on where any extra candidates may be located.
In this very puzzle, one could also identify the Unique Rectangle that occurs with (1,4) in rows 1 and 9, columns 5 and 6. This time there occur two extra candidates (7 and 8) in both of the row 9 ends of the rectangle. One could make the case that 7 and 8 are now a strong pair which will fill these two grid spots. Any grid spot that can be seen by both of these two, can have the 7 and the 8 eliminated from them. This means r8c6<>7, and r9c9<>7. And the puzzle quickly solves from there.
The UR in rows 2 and 3, columns 3 and 8 is much preferred here, as it is simpler, with only one extra candidate (6).
I have learned something else along these lines. The UR must be in only 2 boxes. If it occurs in 4 boxes it becomes technically a Unique Square, and any extra candidates become eliminations in such a case, which again becomes a very valuable solving technique.
In my next posted puzzle I will try to include a Unique Square.
immpy |
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Ajò Dimonios
Joined: 01 May 2017
Posts: 339
Location: Sassari Italy
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| Posted: Sun Jul 23, 2017 8:31 pm Post subject: |
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Hi everyone
Solutions with two step after basics,fish and fins fish.
1) [(3)R4C6-(3=1)R5C4 and (3-4)R4C6=(4)R4C7-(4=1)R5C9 =>contradiction two 1 in line 5=>-3R4C6
2) [(4)R5C8-(4)R23C8=(4)R3C7-(4=1)R7C7 and (4-5)R5C8=(5)R5C5-(5=1)R7C5=>contradiction two 1 in line 7=>-4R5C8=>solution stte.
Ciao a tutti
Paolo |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jul 23, 2017 11:17 pm Post subject: |
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| Quote: | | I'm going to defend the Unique Rectangle as a solving technique |
Why do you need to defend the UR? Maybe I'm missing or misinterpreting something here, but is it under attack? It's considered a standard technique on most sites I've visited that have a section on techniques. |
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immpy
Joined: 06 May 2017
Posts: 571
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| Posted: Mon Jul 24, 2017 3:25 pm Post subject: |
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| Indeed yes it is. Just wanted to reaffirm this after ZeroAssoluto's post. |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Mon Jul 24, 2017 5:31 pm Post subject: |
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UR(14)r23c38 -> 0 solution because, for example :
| Code: | +-----------------+----------------------+-------------------+
| 26 8 5 | 26 14 14 | 3 7 9 |
| 2679 269 14 | 26 3 79 | 8 14 5 |
| 79 3 14 | 8 79 5 | 6 14 2 |
+-----------------+----------------------+-------------------+
| 5 1 23 | 7 6 (34) | (24) 9 8 |
| 269 269 2389 | 145(3) 14589 13489 | 12457 (25) 147 |
| 4 7 89 | (15) 89 2 | (15) 3 6 |
+-----------------+----------------------+-------------------+
| 8 24 7 | 9 4(15) 6 | 245(1) 25 3 |
| 1 49 6 | 4(35) 2 347 | 479(5) 8 47 |
| 3 5 29 | 14 1478 1478 | 29 6 147 |
+-----------------+----------------------+-------------------+
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the set P={3C4, (34)r4c6, (42)r4c7, (25)r5c8, (15)r6c47, 1R7, 5B8, 5R8} of 9 constraints has no solution ! |
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Ajò Dimonios
Joined: 01 May 2017
Posts: 339
Location: Sassari Italy
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| Posted: Mon Jul 24, 2017 6:24 pm Post subject: |
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Hi everyone
| Code: |
+---------------+------------------+----------------+
| 26 8 5 | 26 14 14 | 3 7 9 |
| 2679 269 14 | 26 3 79 | 8 14 5 |
| 679 3 14 | 8 79 5 | 146 14 2 |
+---------------+------------------+----------------+
| 5 1 23 | 7 6 34 | 24 9 8 |
| 269 269 2389 | 1345 14589 13489 | 12457 1245 147 |
| 4 7 89 | 15 89 2 | 15 3 6 |
+---------------+------------------+----------------+
| 8 24 7 | 9 145 6 | 1245 1245 3 |
| 1 49 6 | 345 2 347 | 4579 8 47 |
| 3 5 29 | 14 1478 1478 | 269 26 147 |
+---------------+------------------+----------------+
|
Play this puzzle online at the Daily Sudoku site
This situation is impossible simply because if it is true R2C3 = 1 => R3C3 = 4, R3C8 = 1 and R2C8 = 4. But also R2C3 = 4 => R3C3 = 1, R3C8 = 4 and R2C8 = 1 would have a solution because it does not cause as the first solution no elimination or choice in the other 77 cells in the scheme.Future choices and changes are the same for the two solutions. This means that at least two solutions are true, but this makes the sudoku invalid. For this reason, the alternative hypothesis R3C8 = 6 is valid, which unlocks and resolves the scheme.
Ciao a tutti Paolo
Last edited by Ajò Dimonios on Mon Jul 24, 2017 7:24 pm; edited 1 time in total |
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ZeroAssoluto
Joined: 05 Feb 2017
Posts: 943
Location: Rimini, Italy
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| Posted: Mon Jul 24, 2017 7:05 pm Post subject: |
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| JC Van Hay wrote: | UR(14)r23c38 -> 0 solution because, for example :
| Code: | +-----------------+----------------------+-------------------+
| 26 8 5 | 26 14 14 | 3 7 9 |
| 2679 269 14 | 26 3 79 | 8 14 5 |
| 79 3 14 | 8 79 5 | 6 14 2 |
+-----------------+----------------------+-------------------+
| 5 1 23 | 7 6 (34) | (24) 9 8 |
| 269 269 2389 | 145(3) 14589 13489 | 12457 (25) 147 |
| 4 7 89 | (15) 89 2 | (15) 3 6 |
+-----------------+----------------------+-------------------+
| 8 24 7 | 9 4(15) 6 | 245(1) 25 3 |
| 1 49 6 | 4(35) 2 347 | 479(5) 8 47 |
| 3 5 29 | 14 1478 1478 | 29 6 147 |
+-----------------+----------------------+-------------------+
|
the set P={3C4, (34)r4c6, (42)r4c7, (25)r5c8, (15)r6c47, 1R7, 5B8, 5R8} of 9 constraints has no solution ! |
Hello,
maybe I did not explain well in the previous post.
In general there are two cases:
A- The site proposes schemes with more than one solution, and then you can find a situation where the same 4 pairs of numbers are in the 4 vertices of a rectangle and then you have to proceed with other options.
B- The site proposes schemes with only one solution (as dailysudoku.com does) and then if you are in the situation of my first post, you can safely delete numbers 1.4 from the cell in question using the UR.
It is normal that if r3c8 is not 6 the schema has no solution.
If r3c8 = -6, you would return with 4 pairs to the 4 vertices and you would have no indication (in column, sector, or row) on which number is correct for those 4 cells.
Ciao Gianni |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Jul 24, 2017 8:09 pm Post subject: |
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| Quote: | maybe I did not explain well in the previous post.
In general there are two cases:
A- The site proposes schemes with more than one solution, and then you can find a situation where the same 4 pairs of numbers are in the 4 vertices of a rectangle and then you have to proceed with other options.
B- The site proposes schemes with only one solution (as dailysudoku.com does) and then if you are in the situation of my first post, you can safely delete numbers 1.4 from the cell in question using the UR. |
Gianni,
The casual reader might think that cases A and B occur with equal frequency. I've been on Sudoku forums for 11+ years and haven't seen case B. Sites that are significant sources of puzzles, such as Daily Sudoku here, Brain Bashers, Menneske, Au, Paul's Pages, Sudoku.org.UK and, previously, Vanhegan, all offer puzzles that have one unique solution. All of my online acquaintances automatically assume that the puzzles they see online, whether published by the site or posted by an individual, such as this one by Immpy, have one solution. Occasionally someone posts a non-unique puzzle and someone else catches it and there is no further discussion. |
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ZeroAssoluto
Joined: 05 Feb 2017
Posts: 943
Location: Rimini, Italy
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| Posted: Mon Jul 24, 2017 9:05 pm Post subject: |
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Hi Marty
I think you wont say that you haven't seen case A (more than one solution).
I did not mean to say that there are so many cases with more than one solution and even less those who then have an UR.
But to say that, just because in most cases the schemes have one solution, that if you are in a situation with 4 pairs equal to the 4 vertices of a rectangle, you do not have to go to the end; You know at this point that something is wrong.
Only this
Ciao Gianni |
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Ajò Dimonios
Joined: 01 May 2017
Posts: 339
Location: Sassari Italy
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| Posted: Tue Jul 25, 2017 7:01 am Post subject: |
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Hi everyone
Another solutions with one step. One elimination
| Code: |
+---------------+------------------+----------------+
| 26 8 5 | 26 14 14 | 3 7 9 |
| 2679 269 14 | 26 3 79 | 8 14 5 |
| 679 3 14 | 8 79 5 | 146 146 2 |
+---------------+------------------+----------------+
| 5 1 23 | 7 6 34 | 24 9 8 |
| 269 269 2389 | 1345 14589 13489 | 12457 1245 147 |
| 4 7 89 | 15 89 2 | 15 3 6 |
+---------------+------------------+----------------+
| 8 24 7 | 9 145 6 | 1245 1245 3 |
| 1 49 6 | 345 2 347 | 4579 8 47 |
| 3 5 29 | 14 1478 1478 | 269 26 147 |
+---------------+------------------+----------------+
|
Play this puzzle online at the Daily Sudoku site
Forcing chain
[(1-4)R5C9=(4)R89C9-(4)R8C7; (1)R5C9-(1=5)R6C7-(5)R8C7; (1-7)R5C9=(7)R5C7-(7=9)R8C7-(9=4)R8C2-(4=7)R8C9] and [(1)R5C9-(1)R9C9; (1)R5C9-(1)R6C7=(1)R6C4-(1=4)R9C4-(4=7)R9C9]=>contradiction two singles 7 in box 9 or column 9 =>-1R5C9
Ciao a tutti
Paolo |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Tue Jul 25, 2017 9:29 am Post subject: |
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| Code: | +-----------------+----------------------+-----------------------+
| 26 8 5 | 26 14 14 | 3 7 9 |
| 2679 269 14 | 26 3 79 | 8 14 5 |
| 79 3 14 | 8 79 5 | 146 146 2 |
+-----------------+----------------------+-----------------------+
| 5 1 23 | 7 6 34 | 24 9 8 |
| 269 269 2389 | 1345 4589-1 13489 | 12457 1245 47(1) |
| 4 7 89 | 1-5 89 2 | (15) 3 6 |
+-----------------+----------------------+-----------------------+
| 8 24 7 | 9 4(15) 6 | 245(1) 245(1) 3 |
| 1 49 6 | 34(5) 2 347 | 479-5 8 47 |
| 3 5 29 | 14 1478 1478 | 269 26 47(1) |
+-----------------+----------------------+-----------------------+
5r6c4 1r6c4
1r5c9 1r9c9
1r7c78 1r7c5
5r7c5 5r8c4 -> -{1r5c5, 5r6c4, 5r8c4}; stte |
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Ajò Dimonios
Joined: 01 May 2017
Posts: 339
Location: Sassari Italy
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| Posted: Tue Jul 25, 2017 12:24 pm Post subject: |
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Hi JC
JC Van Hay wrote:
| Code: |
+---------------+------------------+----------------+
| 26 8 5 | 26 14 14 | 3 7 9 |
| 2679 269 14 | 26 3 79 | 8 14 5 |
| 679 3 14 | 8 79 5 | 146 146 2 |
+---------------+------------------+----------------+
| 5 1 23 | 7 6 34 | 24 9 8 |
| 269 269 2389 | 1345 14589 13489 | 12457 1245 147 |
| 4 7 89 | 15 89 2 | 15 3 6 |
+---------------+------------------+----------------+
| 8 24 7 | 9 145 6 | 1245 1245 3 |
| 1 49 6 | 345 2 347 | 4579 8 47 |
| 3 5 29 | 14 1478 1478 | 269 26 147 |
+---------------+------------------+----------------+
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| Quote: |
5r6c4 1r6c4
1r5c9 1r9c9
1r7c78 1r7c5
5r7c5 5r8c4 -> -{1r5c5, 5r6c4, 5r8c4}; stte |
Sorry if I ask you some explanation about the chain. It seems to me that this is a continuous Nice loop, but I can not find the weak inference that binds 1r6c4 to 1r5c9.
Ciao a tutti
Paolo |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Tue Jul 25, 2017 1:56 pm Post subject: |
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Hi Paolo,
Typo : read -5r8c7 instead of -5r8c4 
| Code: | +-----------------+----------------------+-----------------------+
| 26 8 5 | 26 14 14 | 3 7 9 |
| 2679 269 14 | 26 3 79 | 8 14 5 |
| 79 3 14 | 8 79 5 | 146 146 2 |
+-----------------+----------------------+-----------------------+
| 5 1 23 | 7 6 34 | 24 9 8 |
| 269 269 2389 | 1345 4589-1 13489 | 12457 1245 47(1) |
| 4 7 89 | 1-5 89 2 | (15) 3 6 |
+-----------------+----------------------+-----------------------+
| 8 24 7 | 9 4(15) 6 | 245(1) 245(1) 3 |
| 1 49 6 | 34(5) 2 347 | 479-5 8 47 |
| 3 5 29 | 14 1478 1478 | 269 26 47(1) |
+-----------------+----------------------+-----------------------+
5r6c4 1r6c4
1r5c9 1r9c9
1r7c78 1r7c5
5r7c5 5r8c4 -> -{1r5c5, 5r6c4, 5r8c7}; stte |
The chain is a "grouped discontinuous nice loop". In details : reading the matrix representation of the chain from any element, the solutions of the set P={(15)r6c4, 1C9, 1R7, 5B8} of 4 constraints imply the following derived constraints 5r6c4==5r8c4 and 1r5c9==1r7c5 excluding 5r6c4.r8c7 and 1r5c5, respectively.
JC |
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Ajò Dimonios
Joined: 01 May 2017
Posts: 339
Location: Sassari Italy
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| Posted: Tue Jul 25, 2017 8:44 pm Post subject: |
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Hi JC
Perhaps the logic you described to me is also included in the following AIC, which first eliminates 1 in R5C456 and consequently also eliminates 5 in R8C7 and R6C4.
AIC
(1)R5C9=(1)R9C9-(1)R7C78=(1-5)R7C5=(5)R8C4-(5=1)R6C4=>-1R5C456=>R6C4=1;-5R6C4;R6C7=5 and -5R8C7=>solution stte.
Ciao a tutti
Paolo |
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